https://www.causeweb.org/wiki/chance/api.php?action=feedcontributions&user=Laurie+Snell&feedformat=atomChanceWiki - User contributions [en]2022-05-19T19:05:31ZUser contributionsMediaWiki 1.34.0https://www.causeweb.org/wiki/chance/index.php?title=Experiment&diff=670Experiment2005-08-07T01:14:30Z<p>Laurie Snell: </p>
<hr />
<div>:This is an experiment to see if we can put all of Chance-News (July August) on a single page to make it easier to print it out and to make a pdf version.<br />
<br />
A '''Chance News item''' is a discription of an article in the media that uses probability or statistical concepts. <br />
<br />
A Chance News normally consist of:<br />
*The source<br />
*A discussion of the article<br />
*Discussion questions.<br />
<br />
New Chance News items and improvements to previous items are welcome for the Chance Wiki.<br />
<br />
<br />
<br />
== Quotation ==<br />
<blockquote> Numbers are like people; torture them enough and they'll tell you anything.</blockquote><br />
==Forsooth(July-Åugust 2005)<br />
Frank Duckworth, editor of the Royal Statistical Society's newsletter [http://www.therss.org.uk/publications/rssnews.html RSS NEWS] has given us permission to include items from their Forsooth column which they extract forsooth items from media sources. <br />
<br />
Of course we would be happy to have readers add items they feel are worthy of a forsooth!<br />
<br />
From the February 2005 RSS news we have:<br />
<br />
<blockquote>Glasgow's odds (on a white Christmas)<br />
had come in to 8-11, while Aberdeen<br />
was at 5-6, meaning snow in both cities<br />
is considered almost certain.</blockquote><br />
<br />
BBC website<br><br />
22 December 2004<br />
<br />
----<br />
<br />
From the May 2005 RSS News:<br />
<br />
<blockquote>He tried his best--but in the end newborn Casey-James May missed out on a 48 million-to-one record by four minutes. His father Sean, grandfather Dered and great-grandfather Alistair were all born on the same date - March 2. But Casey-James was delivered at 12.04 am on March 3....</blockquote><br />
<br />
Metro<br><br />
10 March 2005<br />
<br />
----<br />
<br />
In the US, those in the poorest households have<br />
nearly four times the risk of death of those in the richest.<br />
<br />
Your World report<br><br />
May 2004<br />
<br />
== Misperception of minorities and immigrants ==<br />
[http://www.stat.columbia.edu/~cook/movabletype/mlm/ Statistical Modeling, Causal Inference, and Social Science] is a statistics Blog. It is maintained by [http://www.stat.columbia.edu/~gelman/ Andrew Gelman], a statistician in the Departments of Statistics and Political Science at Columbia University.<br />
<br />
You will find lots of interesting statistics discussion here. Andrew also gave a [http://www.superdickery.com/stupor/2.html link] to a cartoon in which Superman shows how he would estimate the number of beans in a jar. This also qualifies as a forsooth item.<br />
<br />
In a July 1, 2005 posting Andrew continues an earlier discussion on [http://www.stat.columbia.edu/~cook/movabletype/archives/2005/06/misperception_o.html misperception of minorities]. This earlier discussion resulted from by a note from Tyler Cowen reporting that the March [http://www.harpers.org/HarpersIndex.html Harper's Index] includes the statement:<br />
<br />
<blockquote> -Average percentage of UK population that Britons believe to be immigrants: 21%<br><br />
<br />
-Actual percentage: 8%</blockquote><br />
<br />
Harpers gives as reference the Market & Opinion Research International (MORI). We could not find this statistic on the MORI website but we found something close to it in a Readers Digest (UK) report (November 2000) of a [http://www.mori.com/polls/2000/rd-july.shtml study] "Britain Today - Are We An Intolerant Nation?" that MORI did for the Readers Digest (UK) in 2000. The Digest reports:<br />
<br />
*A massive eight in ten (80%) of British adults believe that refugees come to this country because they regard Britain as 'a soft touch'.<br />
*Two thirds (66%) think that 'there are too many immigrants in Britain'.<br />
* Almost two thirds (63%) feel that 'too much is done to help immigrants'.<br />
* Nearly four in ten (37%) feel that those settling in this country 'should not maintain the culture and lifestyle they had at home'.<br />
<br />
The Digest goes on to say:<br />
<br />
* Respondents grossly overestimated the financial aid asylum seekers receive, believing on average that an asylum seeker gets £113 a week to live on. In fact, a single adult seeking asylum gets £36.54 a week in vouchers to be spent at designated stores. Just £10 may be converted to cash.<br />
* On average the public estimates that 20 per cent of the British population are immigrants. The real figure is around 4 per cent.<br />
* Similarly, they believe that on average 26 per cent of the population belong to an ethnic minority. The real figure is around 7 per cent.<br />
<br />
This last statistic is pretty close to the Harper's Index and the other responses give us some idea why they might over-estimate the percentage of immigrants.<br />
<br />
In the earlier posting, the Harper's Index comments reminded Andrew of an [http://www.washingtonpost.com/ac2/wp-dyn?pagename=article&node=&contentId=A42062-2001Jul10 article] in the Washington Post by Richard Morin (October 8, 1995) in which Morin discussed the results of a Post/Keiser/Harvard [http://www.kff.org/kaiserpolls/1105-index.cfm survey] "Four Americas: Government and Social Policy Through the Eyes of America's Multi-racial and Multi-ethnic Society"<br />
<br />
The Keiser report includes the following data:<br />
<br />
<center>[[Image:Keiser2.jpg]]</center><br />
<br />
Note that, while it is true that the White population significantly underestimated the number of African Americans, Latinos, and Asians, the same is true for each of these groups.<br />
<br />
[http://www.gwu.edu/%7Epsc/people/bio.cfm?name=sides John Sides] sent Andrew the following data on the estimated, and actual percentage of foreign-born residents in each of 20 European countries from the [http:www.europeansocialsurvey.org/ the multi-nation European Social Survey ] :<br />
<br />
<center>[[Image:ForeignBorn.jpg]]</center><br />
<br />
We see that we have signficant overestimation of the number of foreign-born residents, but Germany almost got it right. You will find further discussion on this topic by Andrew and John on the July1, 2005 posting on [http://www.stat.columbia.edu/~gelman/blog/ Andrew's blog].<br />
<br />
DISCUSSION QUESTION:<br />
<br />
(1) What explanations can you think of that might explain this overestimation? Can you suggest additional research that might clarify what is going on here?<br />
<br />
== I was quoting the statistics, I wasn't pretending to be a statistician ==<br />
[http://news.bbc.co.uk/2/hi/health/4679113.stm Sir Roy Meadow struck off by GMC]<br><br />
BBC News, 15 July 2005<br />
<br />
[http://pass.maths.org.uk/issue21/features/clark/ Beyond reasonable doubt]<br><br />
Plus magazine, 2002<br><br />
Helen Joyce<br />
<br />
Multiple sudden infant deaths--coincidence or beyond coincidence<br><br />
Paediatric and Perinatal Epidemiology 2004, 18, 320-326<br><br />
Roy Hill<br />
<br />
___________________________________________________________________________________<br />
<br />
Sir Roy Meadow is a pediatrician, well known for his research in child abuse. The BBC article reports that the UK General Medical Council (GMC) has found Sir Roy guilty of serious professional misconduct and has "struck him off" the medical registry. If upheld under appeal this will prevent Meadow from practicing medicine in the UK.<br />
<br />
This decision was based on a flawed statistical estimate that Meadow made while testifying as an expert witness in a 1999 trial in which a Sally Clark was found guilty of murdering her two baby boys and given a life sentence. <br />
<br />
To understand Meadow's testimony we need to know what SIDS (sudden infant death syndrome) is. The standard definition of SIDS is:<br />
<br />
<blockquote>The sudden death of a baby that is unexpected by history and in whom a thorough post-mortem examination fails to demonstrate an adequate cause of death. </blockquote><br />
<br />
The death of Sally Clark's first baby was reported as a cot death, which is another name for SIDS. Then when her second baby died she was arrested and tried for murdering both her children.<br />
<br />
We were not able to find a transcript for the original trial, but from Lexis Nexis we found transcripts of two appeals that the Clarks made, one in October 2000 and the other in April 2003. The 2003 transcript reported on the statistical testimony in the original trial as follows:<br />
<br />
<blockquote> Professor Meadow was asked about some statistical information as to the happening of two cot deaths within the same family, which at that time was about to be published in a report of a government funded multi-disciplinary research <br />
team, the Confidential Enquiry into Sudden Death in Infancy (CESDI) entitled 'Sudden Unexpected Deaths in Infancy' to which the professor was then writing a Preface. Professor Meadow said that it was 'the most reliable study and easily the largest and in that sense the latest and the best' ever done in this country. <br><br><br />
<br />
It was explained to the jury that there were factors that were suggested as relevant to the chances of a SIDS death within a given family; namely the age of the mother, whether there was a smoker in the household and the absence of a wage-earner in the family.<br><br><br />
<br />
None of these factors had relevance to the Clark family and Professor Meadow was asked if a figure of 1 in 8,543 reflected the risk of there being a single SIDS within such a family. He agreed that it was. A table from the CESDI report was placed before the jury. He was then asked if the report calculated the risk of two infants dying of SIDS in that family by chance. His reply was: 'Yes, you have to multiply 1 in 8,543 times 1 in 8,543 and I think it gives that in the penultimate paragraph. It points out that it's approximately a chance of 1 in 73 million.' <br><br><br />
<br />
It seems that at this point Professor Meadow's voice was dropping and so the figure was repeated and then Professor Meadow added: 'In England, Wales and Scotland there are about say 700,000 live births a year, so it is saying by chance that happening will occur about once every hundred years.' <br><br><br />
<br />
Mr. Spencer [for the prosecution] then pointed to the suspicious features alleged by the Crown in this present case and asked: 'So is this right, not only would the chance be 1 in 73 million but in addition in these two deaths there are features, which would be regarded as suspicious in any event?' He elicited the reply 'I believe so'. <br><br><br />
<br />
All of this evidence was given without objection from the defence but Mr. Bevan (who represented the Appellant at trial and at the first appeal but not at ours) cross--examined the doctor. He put to him figures from other research that suggested that the figure of 1 in 8,543 for a single cot death might be much too high. He then dealt with the chance of two cot deaths and Professor Meadow responded: 'This is why you take what's happened to all the children into account, and that is why you end up saying the chance of the children dying naturally in these circumstances is very, very long odds indeed one in 73 million.' <br />
He then added: <br><br><br />
<br />
'. . . it's the chance of backing that long odds outsider at the Grand National, you know; let's say it's a 80 to 1 chance, <br />
you back the winner last year, then the next year there's another horse at 80 to 1 and it is still 80 to 1 and you back it again <br />
and it wins. Now here we're in a situation that, you know, to get to these odds of 73 million you've got to back that 1 in 80 <br />
chance four years running, so yes, you might be very, very lucky because each time it's just been a 1 in 80 chance and you <br />
know, you've happened to have won it, but the chance of it happening four years running we all know is extraordinarily <br />
unlikely. So it's the same with these deaths. You have to say two unlikely events have happened and together it's very, <br />
very, very unlikely.' <br><br><br />
<br />
The trial judge clearly tried to divert the jury away from reliance on this statistical evidence. He said: 'I should, I think, members of the jury just sound a word of caution about the statistics. However compelling you may find them to be, we do not convict people in these courts on statistics. It would be a terrible day if that were so. If there is one SIDS death in a family, it does not mean that there cannot be another one in the same family.' </blockquote><br />
<br />
Note that Meadow obtained the odds of 73 million to one from the CESDI report so there is some truth to the statement "I was quoting the statistics, I wasn't pretending to be a statistician" that Meadow made to the General Medical Council. Note also that both Meadow and the Judge took this statistic seriously and must have felt that it was evidence that Sally Clark was guilty. This was also true of the press. The Sunday Mail (Queenstand, Australia) had an article titled "Mum killed her babies" in which we read: <br />
<br />
<BLOCKQUOTE>Medical experts gave damning evidence that the odds of both children dying from cot death were 73 million to one.</blockquote><br />
<br />
There are two obvious problems with this 1 in 73 million statistic: (1) Meadow assumed that in a family like the Clarks the events the "first child has a SIDS death" and "the second child has a SIDS death" are independent events. Because of environmental and genetics effects it seems very unlikely this is the case. (2) The 73 million to 1 odds might suggest to the jury that there is a 1 in 73 million chance that Sally Clark is innocent. The medical experts testimonies were very technical and some were contradictory. The 1 in 73 million odds were something the jury would at least feel that they understood. If you gave these odds to your Uncle George and asked him if Sally Clark is guilty he will very likely say "yes".<br />
<br />
The 73 million to 1 odds for SIDS deaths are useless to the jury in assessing guilt unless they are also given the corresponding odds that the deaths were the result of murders. We shall see later that, in this situation, SIDS deaths are about 9 time more likely than murders suggesting that Sally Clark is innocent rather than guilty. <br />
<br />
The Clarks had their first appeal in 2 October 2000. By this time they realized that they had to have their own statisticians as expert witnesses. They chose Ian Evett from the Forensic Science Service and Philip Dawid, Professor of Statistics at University College London. Both of these statisticians have specialized in statistical evidence in the courts. In his report Dawid gave a very clear description of what would be required to obtain a reasonable estimate of the probability of two SIDS deaths in a randomly chosen family with two babies. He emphasized that it would be important also to have some estimate of the variability of this estimate. Then he gave an equally clear discussion on the relevance of this probability, emphasizing the need for the corresponding probability of two murders in a family with two children. His conclusion was:<br />
<br />
<blockquote>The figure ''1 in 73 million'' quoted in Sir Roy Meadow's testimony at trial, as the probability of two babies both dying of SIDS in a family like Sally Clark's, was highly misleading and prejudicial. The value of this probability has not been estimated with anything like the precision suggested, and could well be very much higher. But, more important, the figure was presented with no explanation of the logically correct use of such information - which is very different from what a simple intuitive reaction might suggest. In particular, such a figure could only be useful if compared with a similar figure calculated under the alternative hypothesis that both babies were murdered. Even though assessment of the relevant probabilities may be difficult, there is a clear and well-established statistical logic for combining them and making appropriate inferences from them, which was not appreciated by the court. </blockquote><br />
<br />
These two statisticians were not allowed to appear in the court proceedings but only to have their reports read. <br />
<br />
The Clarks' grounds for appeal included medical and statistical errors. In particular they included Meadow's incorrect calculation and the Judge's failing to warn the jury against the "prosecutor's fallacy".<br />
<br />
Concerning the miscalculation of the odds for two SIDS in a family of two children, the judge remarks that this was already known and all that really mattered was that appearance of two SIDS deaths is unusual.<br />
<br />
The judge then dismisses the prosecutor's fallacy with the remark:<br />
<br />
He [Everett] makes the obvious point that the evidential material in Table 3.58 tells us nothing whatsoever as to the guilt or innocence of the appellant. <br />
<br />
The judge concludes:<br />
<br />
<blockquote> Thus we do not think that the matters raised under Ground 3(a) (the statistical issues) are capable of affecting the safety of the convictions. They do not undermine what was put before the jury or cast a fundamentally different light on it. Even if they had been raised at trial, the most that could be expected to have resulted would be a direction to the jury that the issue was the broad one of rarity, to which the precise degree of probability was unnecessary. </blockquote><br />
<br />
The Judge dismissed the appeal.<br />
<br />
After this the mathematics and statistical communities realized that it was necessary to explain these statistical issues to the legal community and the press. On 23 October Royal Statistics Society addressed these issues in a press release and in January 2002 they sent a letter to the Lord Chamberllor. Both of these are available [http://www.rss.org.uk/main.asp?page=1225 here]. Here is the letter to the Lord Chancelor:<br />
<br />
<blockquote> Dear Lord Chancellor, <br><br><br />
<br />
I am writing to you on behalf of the Royal Statistical Society to express the Society's concern about <br />
some aspects of the presentation of statistical evidence in criminal trials. <br><br><br />
<br />
You will be aware of the considerable public attention aroused by the recent conviction, confirmed on <br />
appeal, of Sally Clark for the murder of her two infants. One focus of the public attention was the <br />
statistical evidence given by a medical expert witness, who drew on a published study to obtain an <br />
estimate of the frequency of sudden infant death syndrome (SIDS, or "cot death") in families having <br />
some of the characteristics of the defendant's family. The witness went on to square this estimate to <br />
obtain a value of 1 in 73 million for the frequency of two cases of SIDS in such a family. This figure had <br />
an immediate and dramatic impact on all media reports of the trial, and it is difficult to believe that it did <br />
not also influence jurors. <br><br><br />
<br />
The calculation leading to 1 in 73 million is invalid. It would only be valid if SIDS cases arose <br />
Independently within families, an assumption that would need to be justified empirically. Not only was <br />
no such empirical justification provided in the case, but there are very strong reasons for supposing that <br />
the assumption is false. There may well be unknown genetic or environmental factors that predispose <br />
families to SIDS, so that a second case within the family becomes much more likely than would be a <br />
case in another, apparently similar, family.<br><br><br />
<br />
A separate concern is that the characteristics used to classify the Clark family were chosen on the basis <br />
of the same data as was used to evaluate the frequency for that classification. This double use of data is <br />
well recognized by statisticians as perilous, since it can lead to subtle yet important biases. <br />
<br />
<br><br><br />
For these reasons, the 1 in 73 million figure cannot be regarded as statistically valid. The Court of <br />
Appeal recognized flaws in its calculation, but seemed to accept it as establishing "... a very broad point, <br />
namely the rarity of double SIDS" [AC judgment, para 138]. However, not only is the error in the 1 in <br />
73 million figure likely to be very large, it is almost certainly in one particular direction - against the <br />
defendant. Moreover, following from the 1 in 73 million figure at the original trial, the expert used a <br />
figure of about 700,000 UK births per year to conclude that "... by chance that happening will occur <br />
every 100 years". This conclusion is fallacious, not only because of the invalidity of the 1 in 73 million <br />
figure, but also because the 1 in 73 million figure relates only to families having some characteristics <br />
matching that of the defendant. This error seems not to have been recognized by the Appeal Court, who <br />
cited it without critical comment [AC judgment para 115]. Leaving aside the matter of validity, figures <br />
such as the 1 in 73 million are very easily misinterpreted. Some press reports at the time stated that this <br />
was the chance that the deaths of Sally Clark's two children were accidental. This (mis-)interpretation is <br />
a serious error of logic known as the Prosecutor's Fallacy . The jury needs to weigh up two competing <br />
explanations for the babies' deaths: SIDS or murder. The fact that two deaths by SIDS is quite unlikely <br />
is, taken alone, of little value. Two deaths by murder may well be even more unlikely. What matters is <br />
the relative likelihood of the deaths under each explanation, not just how unlikely they are under one <br />
explanation. <br><br><br />
<br />
The Prosecutor's Fallacy has been well recognized in the context of DNA profile evidence. Its <br />
commission at trial has led to successful appeals (R v. Deen, 1993; R v. Doheny/Adams 1996). In the <br />
latter judgment, the Court of Appeal put in place guidelines for the presentation of DNA evidence. <br />
However, we are concerned that the seriousness of the problem more generally has not been sufficiently <br />
recognized. In particular, we are concerned that the Appeal Court did not consider it necessary to <br />
examine the expert statistical evidence, but were content with written submissions. <br><br><br />
<br />
The case of R v. Sally Clark is one example of a medical expert witness making a serious statistical <br />
error. Although the Court of Appeal judgment implied a view that the error was unlikely to have had a <br />
profound effect on the outcome of the case, it would be better that the error had not occurred at all. <br />
Although many scientists have some familiarity with statistical methods, statistics remains a specialized <br />
area. The Society urges you to take steps to ensure that statistical evidence is presented only by <br />
appropriately qualified statistical experts, as would be the case for any other form of expert evidence. <br />
Without suggesting that there are simple or uniform answers, the Society would be pleased to be <br />
involved in further discussions on the use and presentation of statistical evidence in courts, and to give <br />
advice on the validation of the expertise of witnesses.<br><br><br />
<br />
Yours sincerely<br> <br />
Professor Peter Green, <br><br />
President, Royal Statistical Society. <br />
</blockquote><br />
<br />
Now that we all agree that we need to know the relative probability that a family with two babies loses them by SIDS deaths or by murder, what are these probabilities?. Roy Hill, Professor of Mathematics at the University of Salford tackled this question. His results were first given in an unpublished paper "Cot death or Murder-weighing the probabilities" presented to the Developmental Physiology Conference, June 2002 (available from the author). Hill published his results in the his article "Multiple sudden infant deaths--coincidence or beyond coincidence?, "Paediatric and Perinatal Epidemiology" 2004, 18, 320-326.<br />
<br />
In the trial the news media made frequent references to "Meadow's law". This law is: "One cot death is a tragedy, two cot deaths is suspicious and three cot deaths is murder". This motivated Hill to test this law by estimating the relative probability of SIDS and murder deaths for the case of 1 baby, 2 babies, and 3 babies. This is a difficult problem since data from different studies give different estimates, the estimates differ over time etc. However Hill did a heroic job of combining all data he could find to come up with reasonable estimates. Here is what he found:<br />
<br />
Regarding the issue of independence Hill concludes:<br />
<br />
<blockquote>In the light of all the data, it seems reasonable to estimate that the risk of SIDS is between 5 and 10 times greater for infants where a sibling has already been a SIDS victim.</blockquote><br />
<br />
As to the relative probabilities of SIDS deaths and murders Hill provides the following estimates:<br />
<br />
(1) An infant is about 17 times more likely to be a SIDS victim than a homicide victim.<br />
<br />
(2) Two infants are about 9 times more likely to be SIDS victims than homicide victims.<br />
<br />
(3) Three infants have about the same probability of being SIDS victims or homicide victims.<br />
<br />
These estimates do not support Meadow's Law. Despite many references to Meadow's Law in the medical journals and the news media, the editor for Hill's article comments that it appears to be due to D.J. and F.J. M Di Maio and seems not to appear in any of Meadow's writings.<br />
<br />
Hill's analysis is used in the very nice article on the Sally Clark case [http://pass.maths.org.uk/issue21/features/clark/ "Beyond reasonable doubt"] by Helen Joyce in ''Plus magazine''. This is a great article to have students read. <br />
<br />
After the failure of their appeal, the Clarks started a campaign to get the news media to support their campaign. They also continued to search for medical explanations for their children's deaths. In the process they found that the prosecutor's pathologist who had performed the autopsies for the two children had withheld the information that their second child had been suffering from a bacterial infection which could have been the cause of a natural death. Recall that his first opinion had been that the first child also was a natural death. This information and the flawed statistics led the Criminal Cases Review Commission, which investigates possible miscarriages of justice, to refer the case back to the courts for another appeal.<br />
<br />
In this appeal the judge ruled that if the bacterial infection information had been known in the original trial, the Sally Clark would probably not have been convicted, and so he allowed the appeal and quashed the convictions freeing Sally Clalrk after two and a half years in jail.. <br />
<br />
The judge also agreed that the statistical evidence was seriously flawed and conclued:<br />
<br />
<blockquote>Thus it seems likely that if this matter had been fully argued before us we would, in all probability, have considered that the statistical evidence provided a quite distinct basis upon which the appeal had to be allowed. </blockquote><br />
<br />
Thus we cannot say that the famous 1 chance in 73 million statistic was responsible for Sally Clark being freed from jail but it is very likely the reason she spent two and a half years in jail.<br />
<br />
For the complete Sally Clark story we recommend the book "Stolen Innocence" by John Batt available at U.K. Amazon. Batt is a lawyer and good friend of the Clarks. He attended the trials and his book tells the Sally Clark story from beginning to end. We also found it interesting to read the transcripts of the 2000 and 2003 appeal. These were not easy to find so we include at the end of this article the Lexis Nexis path to these transcrips.<br />
<br />
Sir Roy Meadow was also the key prosecution witness in two other cases similar to the Sally Clark case: the Angela Canning case and the Trupti Patel case. Roy Hill also wrote an intersting article "Reflections on the cot death cases", ''Significance'', volume 2 (2005), issue 1 in which he discusses the statistical issues in all three cases. <br />
<br />
Finding the 2000 and 2003 transcripts in Lexis Nexis.<br />
<br />
Open Lexis Nexis<br />
<br />
Choose "Legal Research" from the sidebar<br />
<br />
From "Case Law" choose "Get a Case"<br />
<br />
Choose" Commonwealth and Foreign Nations" from the sidebar<br />
<br />
Choose "Sally Clark" for the "Keyword"<br />
<br />
Choose "UK Cases" for the "Source"<br />
<br />
Choose "Previous five years” for the "Date."<br />
<br />
The two "r v Clarks" are the appeals.<br />
<br />
DISCUSSION QUESTIONS:<br />
<br />
(1) Do you think it is easonable not to allow a doctor to practice because of a statistical error in a court case?<br />
<br />
(2) Do you agree with the RSS that statistical evidence should only be provided by statistical experts?<br />
<br />
(3) Give the 73 million to 1 odds to a few of your friends and ask them if they were on the jury, in the absence of any other information, would they think that this makes it is very likely that Sally Clark is guilty?</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Experiment&diff=669Experiment2005-08-07T01:07:14Z<p>Laurie Snell: </p>
<hr />
<div>:This is an experiment to see if we can put all of Chance-News (July August) on a single page to make it easier to print it out and to make a pdf version.<br />
<br />
A '''Chance News item''' is a discription of an article in the media that uses probability or statistical concepts. <br />
<br />
A Chance News normally consist of:<br />
*The source<br />
*A discussion of the article<br />
*Discussion questions.<br />
<br />
New Chance News items and improvements to previous items are welcome for the Chance Wiki.<br />
<br />
<br />
<br />
== Quotation ==<br />
<blockquote> Numbers are like people; torture them enough and they'll tell you anything.</blockquote><br />
==Forsooth(July-Åugust 2005)<br />
Frank Duckworth, editor of the Royal Statistical Society's newsletter [http://www.therss.org.uk/publications/rssnews.html RSS NEWS] has given us permission to include items from their Forsooth column which they extract forsooth items from media sources. <br />
<br />
Of course we would be happy to have readers add items they feel are worthy of a forsooth!<br />
<br />
From the February 2005 RSS news we have:<br />
<br />
<blockquote>Glasgow's odds (on a white Christmas)<br />
had come in to 8-11, while Aberdeen<br />
was at 5-6, meaning snow in both cities<br />
is considered almost certain.</blockquote><br />
<br />
BBC website<br><br />
22 December 2004<br />
<br />
----<br />
<br />
From the May 2005 RSS News:<br />
<br />
<blockquote>He tried his best--but in the end newborn Casey-James May missed out on a 48 million-to-one record by four minutes. His father Sean, grandfather Dered and great-grandfather Alistair were all born on the same date - March 2. But Casey-James was delivered at 12.04 am on March 3....</blockquote><br />
<br />
Metro<br><br />
10 March 2005<br />
<br />
----<br />
<br />
In the US, those in the poorest households have<br />
nearly four times the risk of death of those in the richest.<br />
<br />
Your World report<br><br />
May 2004<br />
<br />
== Misperception of minorities and immigrants ==<br />
[http://www.stat.columbia.edu/~cook/movabletype/mlm/ Statistical Modeling, Causal Inference, and Social Science] is a statistics Blog. It is maintained by [http://www.stat.columbia.edu/~gelman/ Andrew Gelman], a statistician in the Departments of Statistics and Political Science at Columbia University.<br />
<br />
You will find lots of interesting statistics discussion here. Andrew also gave a [http://www.superdickery.com/stupor/2.html link] to a cartoon in which Superman shows how he would estimate the number of beans in a jar. This also qualifies as a forsooth item.<br />
<br />
In a July 1, 2005 posting Andrew continues an earlier discussion on [http://www.stat.columbia.edu/~cook/movabletype/archives/2005/06/misperception_o.html misperception of minorities]. This earlier discussion resulted from by a note from Tyler Cowen reporting that the March [http://www.harpers.org/HarpersIndex.html Harper's Index] includes the statement:<br />
<br />
<blockquote> -Average percentage of UK population that Britons believe to be immigrants: 21%<br><br />
<br />
-Actual percentage: 8%</blockquote><br />
<br />
Harpers gives as reference the Market & Opinion Research International (MORI). We could not find this statistic on the MORI website but we found something close to it in a Readers Digest (UK) report (November 2000) of a [http://www.mori.com/polls/2000/rd-july.shtml study] "Britain Today - Are We An Intolerant Nation?" that MORI did for the Readers Digest (UK) in 2000. The Digest reports:<br />
<br />
*A massive eight in ten (80%) of British adults believe that refugees come to this country because they regard Britain as 'a soft touch'.<br />
*Two thirds (66%) think that 'there are too many immigrants in Britain'.<br />
* Almost two thirds (63%) feel that 'too much is done to help immigrants'.<br />
* Nearly four in ten (37%) feel that those settling in this country 'should not maintain the culture and lifestyle they had at home'.<br />
<br />
The Digest goes on to say:<br />
<br />
* Respondents grossly overestimated the financial aid asylum seekers receive, believing on average that an asylum seeker gets £113 a week to live on. In fact, a single adult seeking asylum gets £36.54 a week in vouchers to be spent at designated stores. Just £10 may be converted to cash.<br />
* On average the public estimates that 20 per cent of the British population are immigrants. The real figure is around 4 per cent.<br />
* Similarly, they believe that on average 26 per cent of the population belong to an ethnic minority. The real figure is around 7 per cent.<br />
<br />
This last statistic is pretty close to the Harper's Index and the other responses give us some idea why they might over-estimate the percentage of immigrants.<br />
<br />
In the earlier posting, the Harper's Index comments reminded Andrew of an [http://www.washingtonpost.com/ac2/wp-dyn?pagename=article&node=&contentId=A42062-2001Jul10 article] in the Washington Post by Richard Morin (October 8, 1995) in which Morin discussed the results of a Post/Keiser/Harvard [http://www.kff.org/kaiserpolls/1105-index.cfm survey] "Four Americas: Government and Social Policy Through the Eyes of America's Multi-racial and Multi-ethnic Society"<br />
<br />
The Keiser report includes the following data:<br />
<br />
<center>[[Image:Keiser2.jpg]]</center><br />
<br />
Note that, while it is true that the White population significantly underestimated the number of African Americans, Latinos, and Asians, the same is true for each of these groups.<br />
<br />
[http://www.gwu.edu/%7Epsc/people/bio.cfm?name=sides John Sides] sent Andrew the following data on the estimated, and actual percentage of foreign-born residents in each of 20 European countries from the [http:www.europeansocialsurvey.org/ the multi-nation European Social Survey ] :<br />
<br />
<center>[[Image:ForeignBorn.jpg]]</center><br />
<br />
We see that we have signficant overestimation of the number of foreign-born residents, but Germany almost got it right. You will find further discussion on this topic by Andrew and John on the July1, 2005 posting on [http://www.stat.columbia.edu/~gelman/blog/ Andrew's blog].<br />
<br />
DISCUSSION QUESTION:<br />
<br />
(1) What explanations can you think of that might explain this overestimation? Can you suggest additional research that might clarify what is going on here?<br />
<br />
== I was quoting the statistics, I wasn't pretending to be a statistician ==<br />
[http://news.bbc.co.uk/2/hi/health/4679113.stm Sir Roy Meadow struck off by GMC]<br><br />
BBC News, 15 July 2005<br />
<br />
[http://pass.maths.org.uk/issue21/features/clark/ Beyond reasonable doubt]<br><br />
Plus magazine, 2002<br><br />
Helen Joyce<br />
<br />
Multiple sudden infant deaths--coincidence or beyond coincidence<br><br />
Paediatric and Perinatal Epidemiology 2004, 18, 320-326<br><br />
Roy Hill<br />
<br />
___________________________________________________________________________________<br />
<br />
Sir Roy Meadow is a pediatrician, well known for his research in child abuse. The BBC article reports that the UK General Medical Council (GMC) has found Sir Roy guilty of serious professional misconduct and has "struck him off" the medical registry. If upheld under appeal this will prevent Meadow from practicing medicine in the UK.<br />
<br />
This decision was based on a flawed statistical estimate that Meadow made while testifying as an expert witness in a 1999 trial in which a Sally Clark was found guilty of murdering her two baby boys and given a life sentence. <br />
<br />
To understand Meadow's testimony we need to know what SIDS (sudden infant death syndrome) is. The standard definition of SIDS is:<br />
<br />
<blockquote>The sudden death of a baby that is unexpected by history and in whom a thorough post-mortem examination fails to demonstrate an adequate cause of death. </blockquote><br />
<br />
The death of Sally Clark's first baby was reported as a cot death, which is another name for SIDS. Then when her second baby died she was arrested and tried for murdering both her children.<br />
<br />
We were not able to find a transcript for the original trial, but from Lexis Nexis we found transcripts of two appeals that the Clarks made, one in October 2000 and the other in April 2003. The 2003 transcript reported on the statistical testimony in the original trial as follows:<br />
<br />
<blockquote> Professor Meadow was asked about some statistical information as to the happening of two cot deaths within the same family, which at that time was about to be published in a report of a government funded multi-disciplinary research <br />
team, the Confidential Enquiry into Sudden Death in Infancy (CESDI) entitled 'Sudden Unexpected Deaths in Infancy' to which the professor was then writing a Preface. Professor Meadow said that it was 'the most reliable study and easily the largest and in that sense the latest and the best' ever done in this country. <br><br><br />
<br />
It was explained to the jury that there were factors that were suggested as relevant to the chances of a SIDS death within a given family; namely the age of the mother, whether there was a smoker in the household and the absence of a wage-earner in the family.<br><br><br />
<br />
None of these factors had relevance to the Clark family and Professor Meadow was asked if a figure of 1 in 8,543 reflected the risk of there being a single SIDS within such a family. He agreed that it was. A table from the CESDI report was placed before the jury. He was then asked if the report calculated the risk of two infants dying of SIDS in that family by chance. His reply was: 'Yes, you have to multiply 1 in 8,543 times 1 in 8,543 and I think it gives that in the penultimate paragraph. It points out that it's approximately a chance of 1 in 73 million.' <br><br><br />
<br />
It seems that at this point Professor Meadow's voice was dropping and so the figure was repeated and then Professor Meadow added: 'In England, Wales and Scotland there are about say 700,000 live births a year, so it is saying by chance that happening will occur about once every hundred years.' <br><br><br />
<br />
Mr. Spencer [for the prosecution] then pointed to the suspicious features alleged by the Crown in this present case and asked: 'So is this right, not only would the chance be 1 in 73 million but in addition in these two deaths there are features, which would be regarded as suspicious in any event?' He elicited the reply 'I believe so'. <br><br><br />
<br />
All of this evidence was given without objection from the defence but Mr. Bevan (who represented the Appellant at trial and at the first appeal but not at ours) cross--examined the doctor. He put to him figures from other research that suggested that the figure of 1 in 8,543 for a single cot death might be much too high. He then dealt with the chance of two cot deaths and Professor Meadow responded: 'This is why you take what's happened to all the children into account, and that is why you end up saying the chance of the children dying naturally in these circumstances is very, very long odds indeed one in 73 million.' <br />
He then added: <br><br><br />
<br />
'. . . it's the chance of backing that long odds outsider at the Grand National, you know; let's say it's a 80 to 1 chance, <br />
you back the winner last year, then the next year there's another horse at 80 to 1 and it is still 80 to 1 and you back it again <br />
and it wins. Now here we're in a situation that, you know, to get to these odds of 73 million you've got to back that 1 in 80 <br />
chance four years running, so yes, you might be very, very lucky because each time it's just been a 1 in 80 chance and you <br />
know, you've happened to have won it, but the chance of it happening four years running we all know is extraordinarily <br />
unlikely. So it's the same with these deaths. You have to say two unlikely events have happened and together it's very, <br />
very, very unlikely.' <br><br><br />
<br />
The trial judge clearly tried to divert the jury away from reliance on this statistical evidence. He said: 'I should, I think, members of the jury just sound a word of caution about the statistics. However compelling you may find them to be, we do not convict people in these courts on statistics. It would be a terrible day if that were so. If there is one SIDS death in a family, it does not mean that there cannot be another one in the same family.' </blockquote><br />
<br />
Note that Meadow obtained the odds of 73 million to one from the CESDI report so there is some truth to the statement "I was quoting the statistics, I wasn't pretending to be a statistician" that Meadow made to the General Medical Council. Note also that both Meadow and the Judge took this statistic seriously and must have felt that it was evidence that Sally Clark was guilty. This was also true of the press. The Sunday Mail (Queenstand, Australia) had an article titled "Mum killed her babies" in which we read: <br />
<br />
<BLOCKQUOTE>Medical experts gave damning evidence that the odds of both children dying from cot death were 73 million to one.</blockquote><br />
<br />
There are two obvious problems with this 1 in 73 million statistic: (1) Meadow assumed that in a family like the Clarks the events the "first child has a SIDS death" and "the second child has a SIDS death" are independent events. Because of environmental and genetics effects it seems very unlikely this is the case. (2) The 73 million to 1 odds might suggest to the jury that there is a 1 in 73 million chance that Sally Clark is innocent. The medical experts testimonies were very technical and some were contradictory. The 1 in 73 million odds were something the jury would at least feel that they understood. If you gave these odds to your Uncle George and asked him if Sally Clark is guilty he will very likely say "yes".<br />
<br />
The 73 million to 1 odds for SIDS deaths are useless to the jury in assessing guilt unless they are also given the corresponding odds that the deaths were the result of murders. We shall see later that, in this situation, SIDS deaths are about 9 time more likely than murders suggesting that Sally Clark is innocent rather than guilty. <br />
<br />
The Clarks had their first appeal in 2 October 2000. By this time they realized that they had to have their own statisticians as expert witnesses. They chose Ian Evett from the Forensic Science Service and Philip Dawid, Professor of Statistics at University College London. Both of these statisticians have specialized in statistical evidence in the courts. In his report Dawid gave a very clear description of what would be required to obtain a reasonable estimate of the probability of two SIDS deaths in a randomly chosen family with two babies. He emphasized that it would be important also to have some estimate of the variability of this estimate. Then he gave an equally clear discussion on the relevance of this probability, emphasizing the need for the corresponding probability of two murders in a family with two children. His conclusion was:<br />
<br />
<blockquote>The figure ''1 in 73 million'' quoted in Sir Roy Meadow's testimony at trial, as the probability of two babies both dying of SIDS in a family like Sally Clark's, was highly misleading and prejudicial. The value of this probability has not been estimated with anything like the precision suggested, and could well be very much higher. But, more important, the figure was presented with no explanation of the logically correct use of such information - which is very different from what a simple intuitive reaction might suggest. In particular, such a figure could only be useful if compared with a similar figure calculated under the alternative hypothesis that both babies were murdered. Even though assessment of the relevant probabilities may be difficult, there is a clear and well-established statistical logic for combining them and making appropriate inferences from them, which was not appreciated by the court. </blockquote><br />
<br />
These two statisticians were not allowed to appear in the court proceedings but only to have their reports read. <br />
<br />
The Clarks' grounds for appeal included medical and statistical errors. In particular they included Meadow's incorrect calculation and the Judge's failing to warn the jury against the "prosecutor's fallacy".<br />
<br />
Concerning the miscalculation of the odds for two SIDS in a family of two children, the judge remarks that this was already known and all that really mattered was that appearance of two SIDS deaths is unusual.<br />
<br />
The judge then dismisses the prosecutor's fallacy with the remark:<br />
<br />
He [Everett] makes the obvious point that the evidential material in Table 3.58 tells us nothing whatsoever as to the guilt or innocence of the appellant. <br />
<br />
The judge concludes:<br />
<br />
<blockquote> Thus we do not think that the matters raised under Ground 3(a) (the statistical issues) are capable of affecting the safety of the convictions. They do not undermine what was put before the jury or cast a fundamentally different light on it. Even if they had been raised at trial, the most that could be expected to have resulted would be a direction to the jury that the issue was the broad one of rarity, to which the precise degree of probability was unnecessary. </blockquote><br />
<br />
The Judge dismissed the appeal.<br />
<br />
After this the mathematics and statistical communities realized that it was necessary to explain these statistical issues to the legal community and the press. On 23 October Royal Statistics Society addressed these issues in a press release and in January 2002 they sent a letter to the Lord Chamberllor. Both of these are available [http://www.rss.org.uk/main.asp?page=1225 here]. Here is the letter to the Lord Chancelor:<br />
<br />
<blockquote> Dear Lord Chancellor, <br><br><br />
<br />
I am writing to you on behalf of the Royal Statistical Society to express the Society's concern about <br />
some aspects of the presentation of statistical evidence in criminal trials. <br><br><br />
<br />
You will be aware of the considerable public attention aroused by the recent conviction, confirmed on <br />
appeal, of Sally Clark for the murder of her two infants. One focus of the public attention was the <br />
statistical evidence given by a medical expert witness, who drew on a published study to obtain an <br />
estimate of the frequency of sudden infant death syndrome (SIDS, or "cot death") in families having <br />
some of the characteristics of the defendant's family. The witness went on to square this estimate to <br />
obtain a value of 1 in 73 million for the frequency of two cases of SIDS in such a family. This figure had <br />
an immediate and dramatic impact on all media reports of the trial, and it is difficult to believe that it did <br />
not also influence jurors. <br><br><br />
<br />
The calculation leading to 1 in 73 million is invalid. It would only be valid if SIDS cases arose <br />
Independently within families, an assumption that would need to be justified empirically. Not only was <br />
no such empirical justification provided in the case, but there are very strong reasons for supposing that <br />
the assumption is false. There may well be unknown genetic or environmental factors that predispose <br />
families to SIDS, so that a second case within the family becomes much more likely than would be a <br />
case in another, apparently similar, family.<br><br><br />
<br />
A separate concern is that the characteristics used to classify the Clark family were chosen on the basis <br />
of the same data as was used to evaluate the frequency for that classification. This double use of data is <br />
well recognized by statisticians as perilous, since it can lead to subtle yet important biases. <br />
<br />
<br><br><br />
For these reasons, the 1 in 73 million figure cannot be regarded as statistically valid. The Court of <br />
Appeal recognized flaws in its calculation, but seemed to accept it as establishing "... a very broad point, <br />
namely the rarity of double SIDS" [AC judgment, para 138]. However, not only is the error in the 1 in <br />
73 million figure likely to be very large, it is almost certainly in one particular direction - against the <br />
defendant. Moreover, following from the 1 in 73 million figure at the original trial, the expert used a <br />
figure of about 700,000 UK births per year to conclude that "... by chance that happening will occur <br />
every 100 years". This conclusion is fallacious, not only because of the invalidity of the 1 in 73 million <br />
figure, but also because the 1 in 73 million figure relates only to families having some characteristics <br />
matching that of the defendant. This error seems not to have been recognized by the Appeal Court, who <br />
cited it without critical comment [AC judgment para 115]. Leaving aside the matter of validity, figures <br />
such as the 1 in 73 million are very easily misinterpreted. Some press reports at the time stated that this <br />
was the chance that the deaths of Sally Clark's two children were accidental. This (mis-)interpretation is <br />
a serious error of logic known as the Prosecutor's Fallacy . The jury needs to weigh up two competing <br />
explanations for the babies' deaths: SIDS or murder. The fact that two deaths by SIDS is quite unlikely <br />
is, taken alone, of little value. Two deaths by murder may well be even more unlikely. What matters is <br />
the relative likelihood of the deaths under each explanation, not just how unlikely they are under one <br />
explanation. <br><br><br />
<br />
The Prosecutor's Fallacy has been well recognized in the context of DNA profile evidence. Its <br />
commission at trial has led to successful appeals (R v. Deen, 1993; R v. Doheny/Adams 1996). In the <br />
latter judgment, the Court of Appeal put in place guidelines for the presentation of DNA evidence. <br />
However, we are concerned that the seriousness of the problem more generally has not been sufficiently <br />
recognized. In particular, we are concerned that the Appeal Court did not consider it necessary to <br />
examine the expert statistical evidence, but were content with written submissions. <br><br><br />
<br />
The case of R v. Sally Clark is one example of a medical expert witness making a serious statistical <br />
error. Although the Court of Appeal judgment implied a view that the error was unlikely to have had a <br />
profound effect on the outcome of the case, it would be better that the error had not occurred at all. <br />
Although many scientists have some familiarity with statistical methods, statistics remains a specialized <br />
area. The Society urges you to take steps to ensure that statistical evidence is presented only by <br />
appropriately qualified statistical experts, as would be the case for any other form of expert evidence. <br />
Without suggesting that there are simple or uniform answers, the Society would be pleased to be <br />
involved in further discussions on the use and presentation of statistical evidence in courts, and to give <br />
advice on the validation of the expertise of witnesses.<br><br><br />
<br />
Yours sincerely<br> <br />
Professor Peter Green, <br><br />
President, Royal Statistical Society. <br />
</blockquote><br />
<br />
Now that we all agree that we need to know the relative probability that a family with two babies loses them by SIDS deaths or by murder, what are these probabilities?. Roy Hill, Professor of Mathematics at the University of Salford tackled this question. His results were first given in an unpublished paper "Cot death or Murder-weighing the probabilities" presented to the Developmental Physiology Conference, June 2002 (available from the author). Hill published his results in the his article "Multiple sudden infant deaths--coincidence or beyond coincidence?, "Paediatric and Perinatal Epidemiology" 2004, 18, 320-326.<br />
<br />
In the trial the news media made frequent references to "Meadow's law". This law is: "One cot death is a tragedy, two cot deaths is suspicious and three cot deaths is murder". This motivated Hill to test this law by estimating the relative probability of SIDS and murder deaths for the case of 1 baby, 2 babies, and 3 babies. This is a difficult problem since data from different studies give different estimates, the estimates differ over time etc. However Hill did a heroic job of combining all data he could find to come up with reasonable estimates. Here is what he found:<br />
<br />
Regarding the issue of independence Hill concludes:<br />
<br />
<blockquote>In the light of all the data, it seems reasonable to estimate that the risk of SIDS is between 5 and 10 times greater for infants where a sibling has already been a SIDS victim.</blockquote><br />
<br />
As to the relative probabilities of SIDS deaths and murders Hill provides the following estimates:<br />
<br />
(1) An infant is about 17 times more likely to be a SIDS victim than a homicide victim.<br />
<br />
(2) Two infants are about 9 times more likely to be SIDS victims than homicide victims.<br />
<br />
(3) Three infants have about the same probability of being SIDS victims or homicide victims.<br />
<br />
These estimates do not support Meadow's Law. Despite many references to Meadow's Law in the medical journals and the news media, the editor for Hill's article comments that it appears to be due to D.J. and F.J. M Di Maio and seems not to appear in any of Meadow's writings.<br />
<br />
Hill's analysis is used in the very nice article on the Sally Clark case [http://pass.maths.org.uk/issue21/features/clark/ "Beyond reasonable doubt"] by Helen Joyce in ''Plus magazine''. This is a great article to have students read. <br />
<br />
After the failure of their appeal, the Clarks started a campaign to get the news media to support their campaign. They also continued to search for medical explanations for their children's deaths. In the process they found that the prosecutor's pathologist who had performed the autopsies for the two children had withheld the information that their second child had been suffering from a bacterial infection which could have been the cause of a natural death. Recall that his first opinion had been that the first child also was a natural death. This information and the flawed statistics led the Criminal Cases Review Commission, which investigates possible miscarriages of justice, to refer the case back to the courts for another appeal.<br />
<br />
In this appeal the judge ruled that if the bacterial infection information had been known in the original trial, the Sally Clark would probably not have been convicted, and so he allowed the appeal and quashed the convictions freeing Sally Clalrk after two and a half years in jail.. <br />
<br />
The judge also agreed that the statistical evidence was seriously flawed and conclued:<br />
<br />
<blockquote>Thus it seems likely that if this matter had been fully argued before us we would, in all probability, have considered that the statistical evidence provided a quite distinct basis upon which the appeal had to be allowed. </blockquote><br />
<br />
Thus we cannot say that the famous 1 chance in 73 million statistic was responsible for Sally Clark being freed from jail but it is very likely the reason she spent two and a half years in jail.<br />
<br />
For the complete Sally Clark story we recommend the book "Stolen Innocence" by John Batt available at U.K. Amazon. Batt is a lawyer and good friend of the Clarks. He attended the trials and his book tells the Sally Clark story from beginning to end. We also found it interesting to read the transcripts of the 2000 and 2003 appeal. These were not easy to find so we include at the end of this article the Lexis Nexis path to these transcrips.<br />
<br />
Sir Roy Meadow was also the key prosecution witness in two other cases similar to the Sally Clark case: the Angela Canning case and the Trupti Patel case. Roy Hill also wrote an intersting article "Reflections on the cot death cases", ''Significance'', volume 2 (2005), issue 1 in which he discusses the statistical issues in all three cases. <br />
<br />
Finding the 2000 and 2003 transcripts in Lexis Nexis.<br />
<br />
Open Lexis Nexis<br />
<br />
Choose "Legal Research" from the sidebar<br />
<br />
From "Case Law" choose "Get a Case"<br />
<br />
Choose" Commonwealth and Foreign Nations" from the sidebar<br />
<br />
Choose "Sally Clark" for the "Keyword"<br />
<br />
Choose "UK Cases" for the "Source"<br />
<br />
Choose "Previous five years” for the "Date."<br />
<br />
The two "r v Clarks" are the appeals.<br />
<br />
DISCUSSION QUESTIONS:<br />
<br />
(1) Do you think it is easonable not to allow a doctor to practice because of a statistical error in a court case?<br />
<br />
(2) Do you agree with the RSS that statistical evidence should only be provided by statistical experts?<br />
<br />
(3) Give the 73 million to 1 odds to a few of your friends and ask them if they were on the jury, in the absence of any other information, would they think that this makes it is very likely that Sally Clark is guilty?<br />
<br />
bsite with over 7,000 recipes.<br />
*[http://www.stratsplace.com/rogov/art_writing_recipes.html ''The Art of Writing Workable</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Experiment&diff=668Experiment2005-08-07T00:45:05Z<p>Laurie Snell: </p>
<hr />
<div>:This is an experiment to see if we can put all of Chance-News (July August) on a single page to make it easier to print it out and to make a pdf version.<br />
<br />
A '''Chance News item''' is a discription of an article in the media that uses probability or statistical concepts. <br />
<br />
A Chance News normally consist of:<br />
*The source<br />
*A discussion of the article<br />
*Discussion questions.<br />
<br />
New Chance News items and improvements to previous items are welcome for the Chance Wiki.<br />
<br />
<br />
<br />
== Quotation ==<br />
<blockquote> Numbers are like people; torture them enough and they'll tell you anything.</blockquote><br />
==Forsooth(July-Åugust 2005)<br />
Frank Duckworth, editor of the Royal Statistical Society's newsletter [http://www.therss.org.uk/publications/rssnews.html RSS NEWS] has given us permission to include items from their Forsooth column which they extract forsooth items from media sources. <br />
<br />
Of course we would be happy to have readers add items they feel are worthy of a forsooth!<br />
<br />
From the February 2005 RSS news we have:<br />
<br />
<blockquote>Glasgow's odds (on a white Christmas)<br />
had come in to 8-11, while Aberdeen<br />
was at 5-6, meaning snow in both cities<br />
is considered almost certain.</blockquote><br />
<br />
BBC website<br><br />
22 December 2004<br />
<br />
----<br />
<br />
From the May 2005 RSS News:<br />
<br />
<blockquote>He tried his best--but in the end newborn Casey-James May missed out on a 48 million-to-one record by four minutes. His father Sean, grandfather Dered and great-grandfather Alistair were all born on the same date - March 2. But Casey-James was delivered at 12.04 am on March 3....</blockquote><br />
<br />
Metro<br><br />
10 March 2005<br />
<br />
----<br />
<br />
In the US, those in the poorest households have<br />
nearly four times the risk of death of those in the richest.<br />
<br />
Your World report<br><br />
May 2004<br />
<br />
== Misperception of minorities and immigrants ==<br />
[http://www.stat.columbia.edu/~cook/movabletype/mlm/ Statistical Modeling, Causal Inference, and Social Science] is a statistics Blog. It is maintained by [http://www.stat.columbia.edu/~gelman/ Andrew Gelman], a statistician in the Departments of Statistics and Political Science at Columbia University.<br />
<br />
You will find lots of interesting statistics discussion here. Andrew also gave a [http://www.superdickery.com/stupor/2.html link] to a cartoon in which Superman shows how he would estimate the number of beans in a jar. This also qualifies as a forsooth item.<br />
<br />
In a July 1, 2005 posting Andrew continues an earlier discussion on [http://www.stat.columbia.edu/~cook/movabletype/archives/2005/06/misperception_o.html misperception of minorities]. This earlier discussion resulted from by a note from Tyler Cowen reporting that the March [http://www.harpers.org/HarpersIndex.html Harper's Index] includes the statement:<br />
<br />
<blockquote> -Average percentage of UK population that Britons believe to be immigrants: 21%<br><br />
<br />
-Actual percentage: 8%</blockquote><br />
<br />
Harpers gives as reference the Market & Opinion Research International (MORI). We could not find this statistic on the MORI website but we found something close to it in a Readers Digest (UK) report (November 2000) of a [http://www.mori.com/polls/2000/rd-july.shtml study] "Britain Today - Are We An Intolerant Nation?" that MORI did for the Readers Digest (UK) in 2000. The Digest reports:<br />
<br />
*A massive eight in ten (80%) of British adults believe that refugees come to this country because they regard Britain as 'a soft touch'.<br />
*Two thirds (66%) think that 'there are too many immigrants in Britain'.<br />
* Almost two thirds (63%) feel that 'too much is done to help immigrants'.<br />
* Nearly four in ten (37%) feel that those settling in this country 'should not maintain the culture and lifestyle they had at home'.<br />
<br />
The Digest goes on to say:<br />
<br />
* Respondents grossly overestimated the financial aid asylum seekers receive, believing on average that an asylum seeker gets £113 a week to live on. In fact, a single adult seeking asylum gets £36.54 a week in vouchers to be spent at designated stores. Just £10 may be converted to cash.<br />
* On average the public estimates that 20 per cent of the British population are immigrants. The real figure is around 4 per cent.<br />
* Similarly, they believe that on average 26 per cent of the population belong to an ethnic minority. The real figure is around 7 per cent.<br />
<br />
This last statistic is pretty close to the Harper's Index and the other responses give us some idea why they might over-estimate the percentage of immigrants.<br />
<br />
In the earlier posting, the Harper's Index comments reminded Andrew of an [http://www.washingtonpost.com/ac2/wp-dyn?pagename=article&node=&contentId=A42062-2001Jul10 article] in the Washington Post by Richard Morin (October 8, 1995) in which Morin discussed the results of a Post/Keiser/Harvard [http://www.kff.org/kaiserpolls/1105-index.cfm survey] "Four Americas: Government and Social Policy Through the Eyes of America's Multi-racial and Multi-ethnic Society"<br />
<br />
The Keiser report includes the following data:<br />
<br />
<center>[[Image:Keiser2.jpg]]</center><br />
<br />
Note that, while it is true that the White population significantly underestimated the number of African Americans, Latinos, and Asians, the same is true for each of these groups.<br />
<br />
[http://www.gwu.edu/%7Epsc/people/bio.cfm?name=sides John Sides] sent Andrew the following data on the estimated, and actual percentage of foreign-born residents in each of 20 European countries from the [http:www.europeansocialsurvey.org/ the multi-nation European Social Survey ] :<br />
<br />
<center>[[Image:ForeignBorn.jpg]]</center><br />
<br />
We see that we have signficant overestimation of the number of foreign-born residents, but Germany almost got it right. You will find further discussion on this topic by Andrew and John on the July1, 2005 posting on [http://www.stat.columbia.edu/~gelman/blog/ Andrew's blog].<br />
<br />
DISCUSSION QUESTION:<br />
<br />
(1) What explanations can you think of that might explain this overestimation? Can you suggest additional research that might clarify what is going on here?<br />
<br />
== I was quoting the statistics, I wasn't pretending to be a statistician ==<br />
[http://news.bbc.co.uk/2/hi/health/4679113.stm Sir Roy Meadow struck off by GMC]<br><br />
BBC News, 15 July 2005<br />
<br />
[http://pass.maths.org.uk/issue21/features/clark/ Beyond reasonable doubt]<br><br />
Plus magazine, 2002<br><br />
Helen Joyce<br />
<br />
Multiple sudden infant deaths--coincidence or beyond coincidence<br><br />
Paediatric and Perinatal Epidemiology 2004, 18, 320-326<br><br />
Roy Hill<br />
<br />
___________________________________________________________________________________<br />
<br />
Sir Roy Meadow is a pediatrician, well known for his research in child abuse. The BBC article reports that the UK General Medical Council (GMC) has found Sir Roy guilty of serious professional misconduct and has "struck him off" the medical registry. If upheld under appeal this will prevent Meadow from practicing medicine in the UK.<br />
<br />
This decision was based on a flawed statistical estimate that Meadow made while testifying as an expert witness in a 1999 trial in which a Sally Clark was found guilty of murdering her two baby boys and given a life sentence. <br />
<br />
To understand Meadow's testimony we need to know what SIDS (sudden infant death syndrome) is. The standard definition of SIDS is:<br />
<br />
<blockquote>The sudden death of a baby that is unexpected by history and in whom a thorough post-mortem examination fails to demonstrate an adequate cause of death. </blockquote><br />
<br />
The death of Sally Clark's first baby was reported as a cot death, which is another name for SIDS. Then when her second baby died she was arrested and tried for murdering both her children.<br />
<br />
We were not able to find a transcript for the original trial, but from Lexis Nexis we found transcripts of two appeals that the Clarks made, one in October 2000 and the other in April 2003. The 2003 transcript reported on the statistical testimony in the original trial as follows:<br />
<br />
<blockquote> Professor Meadow was asked about some statistical information as to the happening of two cot deaths within the same family, which at that time was about to be published in a report of a government funded multi-disciplinary research <br />
team, the Confidential Enquiry into Sudden Death in Infancy (CESDI) entitled 'Sudden Unexpected Deaths in Infancy' to which the professor was then writing a Preface. Professor Meadow said that it was 'the most reliable study and easily the largest and in that sense the latest and the best' ever done in this country. <br><br><br />
<br />
It was explained to the jury that there were factors that were suggested as relevant to the chances of a SIDS death within a given family; namely the age of the mother, whether there was a smoker in the household and the absence of a wage-earner in the family.<br><br><br />
<br />
None of these factors had relevance to the Clark family and Professor Meadow was asked if a figure of 1 in 8,543 reflected the risk of there being a single SIDS within such a family. He agreed that it was. A table from the CESDI report was placed before the jury. He was then asked if the report calculated the risk of two infants dying of SIDS in that family by chance. His reply was: 'Yes, you have to multiply 1 in 8,543 times 1 in 8,543 and I think it gives that in the penultimate paragraph. It points out that it's approximately a chance of 1 in 73 million.' <br><br><br />
<br />
It seems that at this point Professor Meadow's voice was dropping and so the figure was repeated and then Professor Meadow added: 'In England, Wales and Scotland there are about say 700,000 live births a year, so it is saying by chance that happening will occur about once every hundred years.' <br><br><br />
<br />
Mr. Spencer [for the prosecution] then pointed to the suspicious features alleged by the Crown in this present case and asked: 'So is this right, not only would the chance be 1 in 73 million but in addition in these two deaths there are features, which would be regarded as suspicious in any event?' He elicited the reply 'I believe so'. <br><br><br />
<br />
All of this evidence was given without objection from the defence but Mr. Bevan (who represented the Appellant at trial and at the first appeal but not at ours) cross--examined the doctor. He put to him figures from other research that suggested that the figure of 1 in 8,543 for a single cot death might be much too high. He then dealt with the chance of two cot deaths and Professor Meadow responded: 'This is why you take what's happened to all the children into account, and that is why you end up saying the chance of the children dying naturally in these circumstances is very, very long odds indeed one in 73 million.' <br />
He then added: <br><br><br />
<br />
'. . . it's the chance of backing that long odds outsider at the Grand National, you know; let's say it's a 80 to 1 chance, <br />
you back the winner last year, then the next year there's another horse at 80 to 1 and it is still 80 to 1 and you back it again <br />
and it wins. Now here we're in a situation that, you know, to get to these odds of 73 million you've got to back that 1 in 80 <br />
chance four years running, so yes, you might be very, very lucky because each time it's just been a 1 in 80 chance and you <br />
know, you've happened to have won it, but the chance of it happening four years running we all know is extraordinarily <br />
unlikely. So it's the same with these deaths. You have to say two unlikely events have happened and together it's very, <br />
very, very unlikely.' <br><br><br />
<br />
The trial judge clearly tried to divert the jury away from reliance on this statistical evidence. He said: 'I should, I think, members of the jury just sound a word of caution about the statistics. However compelling you may find them to be, we do not convict people in these courts on statistics. It would be a terrible day if that were so. If there is one SIDS death in a family, it does not mean that there cannot be another one in the same family.' </blockquote><br />
<br />
Note that Meadow obtained the odds of 73 million to one from the CESDI report so there is some truth to the statement "I was quoting the statistics, I wasn't pretending to be a statistician" that Meadow made to the General Medical Council. Note also that both Meadow and the Judge took this statistic seriously and must have felt that it was evidence that Sally Clark was guilty. This was also true of the press. The Sunday Mail (Queenstand, Australia) had an article titled "Mum killed her babies" in which we read: <br />
<br />
<BLOCKQUOTE>Medical experts gave damning evidence that the odds of both children dying from cot death were 73 million to one.</blockquote><br />
<br />
There are two obvious problems with this 1 in 73 million statistic: (1) Meadow assumed that in a family like the Clarks the events the "first child has a SIDS death" and "the second child has a SIDS death" are independent events. Because of environmental and genetics effects it seems very unlikely this is the case. (2) The 73 million to 1 odds might suggest to the jury that there is a 1 in 73 million chance that Sally Clark is innocent. The medical experts testimonies were very technical and some were contradictory. The 1 in 73 million odds were something the jury would at least feel that they understood. If you gave these odds to your Uncle George and asked him if Sally Clark is guilty he will very likely say "yes".<br />
<br />
The 73 million to 1 odds for SIDS deaths are useless to the jury in assessing guilt unless they are also given the corresponding odds that the deaths were the result of murders. We shall see later that, in this situation, SIDS deaths are about 9 time more likely than murders suggesting that Sally Clark is innocent rather than guilty. <br />
<br />
The Clarks had their first appeal in 2 October 2000. By this time they realized that they had to have their own statisticians as expert witnesses. They chose Ian Evett from the Forensic Science Service and Philip Dawid, Professor of Statistics at University College London. Both of these statisticians have specialized in statistical evidence in the courts. In his report Dawid gave a very clear description of what would be required to obtain a reasonable estimate of the probability of two SIDS deaths in a randomly chosen family with two babies. He emphasized that it would be important also to have some estimate of the variability of this estimate. Then he gave an equally clear discussion on the relevance of this probability, emphasizing the need for the corresponding probability of two murders in a family with two children. His conclusion was:<br />
<br />
<blockquote>The figure ''1 in 73 million'' quoted in Sir Roy Meadow's testimony at trial, as the probability of two babies both dying of SIDS in a family like Sally Clark's, was highly misleading and prejudicial. The value of this probability has not been estimated with anything like the precision suggested, and could well be very much higher. But, more important, the figure was presented with no explanation of the logically correct use of such information - which is very different from what a simple intuitive reaction might suggest. In particular, such a figure could only be useful if compared with a similar figure calculated under the alternative hypothesis that both babies were murdered. Even though assessment of the relevant probabilities may be difficult, there is a clear and well-established statistical logic for combining them and making appropriate inferences from them, which was not appreciated by the court. </blockquote><br />
<br />
These two statisticians were not allowed to appear in the court proceedings but only to have their reports read. <br />
<br />
The Clarks' grounds for appeal included medical and statistical errors. In particular they included Meadow's incorrect calculation and the Judge's failing to warn the jury against the "prosecutor's fallacy".<br />
<br />
Concerning the miscalculation of the odds for two SIDS in a family of two children, the judge remarks that this was already known and all that really mattered was that appearance of two SIDS deaths is unusual.<br />
<br />
The judge then dismisses the prosecutor's fallacy with the remark:<br />
<br />
He [Everett] makes the obvious point that the evidential material in Table 3.58 tells us nothing whatsoever as to the guilt or innocence of the appellant. <br />
<br />
The judge concludes:<br />
<br />
<blockquote> Thus we do not think that the matters raised under Ground 3(a) (the statistical issues) are capable of affecting the safety of the convictions. They do not undermine what was put before the jury or cast a fundamentally different light on it. Even if they had been raised at trial, the most that could be expected to have resulted would be a direction to the jury that the issue was the broad one of rarity, to which the precise degree of probability was unnecessary. </blockquote><br />
<br />
The Judge dismissed the appeal.<br />
<br />
After this the mathematics and statistical communities realized that it was necessary to explain these statistical issues to the legal community and the press. On 23 October Royal Statistics Society addressed these issues in a press release and in January 2002 they sent a letter to the Lord Chamberllor. Both of these are available [http://www.rss.org.uk/main.asp?page=1225 here]. Here is the letter to the Lord Chancelor:<br />
<br />
<blockquote> Dear Lord Chancellor, <br><br><br />
<br />
I am writing to you on behalf of the Royal Statistical Society to express the Society's concern about <br />
some aspects of the presentation of statistical evidence in criminal trials. <br><br><br />
<br />
You will be aware of the considerable public attention aroused by the recent conviction, confirmed on <br />
appeal, of Sally Clark for the murder of her two infants. One focus of the public attention was the <br />
statistical evidence given by a medical expert witness, who drew on a published study to obtain an <br />
estimate of the frequency of sudden infant death syndrome (SIDS, or "cot death") in families having <br />
some of the characteristics of the defendant's family. The witness went on to square this estimate to <br />
obtain a value of 1 in 73 million for the frequency of two cases of SIDS in such a family. This figure had <br />
an immediate and dramatic impact on all media reports of the trial, and it is difficult to believe that it did <br />
not also influence jurors. <br><br><br />
<br />
The calculation leading to 1 in 73 million is invalid. It would only be valid if SIDS cases arose <br />
Independently within families, an assumption that would need to be justified empirically. Not only was <br />
no such empirical justification provided in the case, but there are very strong reasons for supposing that <br />
the assumption is false. There may well be unknown genetic or environmental factors that predispose <br />
families to SIDS, so that a second case within the family becomes much more likely than would be a <br />
case in another, apparently similar, family.<br><br><br />
<br />
A separate concern is that the characteristics used to classify the Clark family were chosen on the basis <br />
of the same data as was used to evaluate the frequency for that classification. This double use of data is <br />
well recognized by statisticians as perilous, since it can lead to subtle yet important biases. <br />
<br />
<br><br><br />
For these reasons, the 1 in 73 million figure cannot be regarded as statistically valid. The Court of <br />
Appeal recognized flaws in its calculation, but seemed to accept it as establishing "... a very broad point, <br />
namely the rarity of double SIDS" [AC judgment, para 138]. However, not only is the error in the 1 in <br />
73 million figure likely to be very large, it is almost certainly in one particular direction - against the <br />
defendant. Moreover, following from the 1 in 73 million figure at the original trial, the expert used a <br />
figure of about 700,000 UK births per year to conclude that "... by chance that happening will occur <br />
every 100 years". This conclusion is fallacious, not only because of the invalidity of the 1 in 73 million <br />
figure, but also because the 1 in 73 million figure relates only to families having some characteristics <br />
matching that of the defendant. This error seems not to have been recognized by the Appeal Court, who <br />
cited it without critical comment [AC judgment para 115]. Leaving aside the matter of validity, figures <br />
such as the 1 in 73 million are very easily misinterpreted. Some press reports at the time stated that this <br />
was the chance that the deaths of Sally Clark's two children were accidental. This (mis-)interpretation is <br />
a serious error of logic known as the Prosecutor's Fallacy . The jury needs to weigh up two competing <br />
explanations for the babies' deaths: SIDS or murder. The fact that two deaths by SIDS is quite unlikely <br />
is, taken alone, of little value. Two deaths by murder may well be even more unlikely. What matters is <br />
the relative likelihood of the deaths under each explanation, not just how unlikely they are under one <br />
explanation. <br><br><br />
<br />
The Prosecutor's Fallacy has been well recognized in the context of DNA profile evidence. Its <br />
commission at trial has led to successful appeals (R v. Deen, 1993; R v. Doheny/Adams 1996). In the <br />
latter judgment, the Court of Appeal put in place guidelines for the presentation of DNA evidence. <br />
However, we are concerned that the seriousness of the problem more generally has not been sufficiently <br />
recognized. In particular, we are concerned that the Appeal Court did not consider it necessary to <br />
examine the expert statistical evidence, but were content with written submissions. <br><br><br />
<br />
The case of R v. Sally Clark is one example of a medical expert witness making a serious statistical <br />
error. Although the Court of Appeal judgment implied a view that the error was unlikely to have had a <br />
profound effect on the outcome of the case, it would be better that the error had not occurred at all. <br />
Although many scientists have some familiarity with statistical methods, statistics remains a specialized <br />
area. The Society urges you to take steps to ensure that statistical evidence is presented only by <br />
appropriately qualified statistical experts, as would be the case for any other form of expert evidence. <br />
Without suggesting that there are simple or uniform answers, the Society would be pleased to be <br />
involved in further discussions on the use and presentation of statistical evidence in courts, and to give <br />
advice on the validation of the expertise of witnesses.<br><br><br />
<br />
Yours sincerely<br> <br />
Professor Peter Green, <br><br />
President, Royal Statistical Society. <br />
</blockquote><br />
<br />
Now that we all agree that we need to know the relative probability that a family with two babies loses them by SIDS deaths or by murder, what are these probabilities?. Roy Hill, Professor of Mathematics at the University of Salford tackled this question. His results were first given in an unpublished paper "Cot death or Murder-weighing the probabilities" presented to the Developmental Physiology Conference, June 2002 (available from the author). Hill published his results in the his article "Multiple sudden infant deaths--coincidence or beyond coincidence?, "Paediatric and Perinatal Epidemiology" 2004, 18, 320-326.<br />
<br />
In the trial the news media made frequent references to "Meadow's law". This law is: "One cot death is a tragedy, two cot deaths is suspicious and three cot deaths is murder". This motivated Hill to test this law by estimating the relative probability of SIDS and murder deaths for the case of 1 baby, 2 babies, and 3 babies. This is a difficult problem since data from different studies give different estimates, the estimates differ over time etc. However Hill did a heroic job of combining all data he could find to come up with reasonable estimates. Here is what he found:<br />
<br />
Regarding the issue of independence Hill concludes:<br />
<br />
<blockquote>In the light of all the data, it seems reasonable to estimate that the risk of SIDS is between 5 and 10 times greater for infants where a sibling has already been a SIDS victim.</blockquote><br />
<br />
As to the relative probabilities of SIDS deaths and murders Hill provides the following estimates:<br />
<br />
(1) An infant is about 17 times more likely to be a SIDS victim than a homicide victim.<br />
<br />
(2) Two infants are about 9 times more likely to be SIDS victims than homicide victims.<br />
<br />
(3) Three infants have about the same probability of being SIDS victims or homicide victims.<br />
<br />
These estimates do not support Meadow's Law. Despite many references to Meadow's Law in the medical journals and the news media, the editor for Hill's article comments that it appears to be due to D.J. and F.J. M Di Maio and seems not to appear in any of Meadow's writings.<br />
<br />
Hill's analysis is used in the very nice article on the Sally Clark case [http://pass.maths.org.uk/issue21/features/clark/ "Beyond reasonable doubt"] by Helen Joyce in ''Plus magazine''. This is a great article to have students read. <br />
<br />
After the failure of their appeal, the Clarks started a campaign to get the news media to support their campaign. They also continued to search for medical explanations for their children's deaths. In the process they found that the prosecutor's pathologist who had performed the autopsies for the two children had withheld the information that their second child had been suffering from a bacterial infection which could have been the cause of a natural death. Recall that his first opinion had been that the first child also was a natural death. This information and the flawed statistics led the Criminal Cases Review Commission, which investigates possible miscarriages of justice, to refer the case back to the courts for another appeal.<br />
<br />
In this appeal the judge ruled that if the bacterial infection information had been known in the original trial, the Sally Clark would probably not have been convicted, and so he allowed the appeal and quashed the convictions freeing Sally Clalrk after two and a half years in jail.. <br />
<br />
The judge also agreed that the statistical evidence was seriously flawed and conclued:<br />
<br />
<blockquote>Thus it seems likely that if this matter had been fully argued before us we would, in all probability, have considered that the statistical evidence provided a quite distinct basis upon which the appeal had to be allowed. </blockquote><br />
<br />
Thus we cannot say that the famous 1 chance in 73 million statistic was responsible for Sally Clark being freed from jail but it is very likely the reason she spent two and a half years in jail.<br />
<br />
For the complete Sally Clark story we recommend the book "Stolen Innocence" by John Batt available at U.K. Amazon. Batt is a lawyer and good friend of the Clarks. He attended the trials and his book tells the Sally Clark story from beginning to end. We also found it interesting to read the transcripts of the 2000 and 2003 appeal. These were not easy to find so we include at the end of this article the Lexis Nexis path to these transcrips.<br />
<br />
Sir Roy Meadow was also the key prosecution witness in two other cases similar to the Sally Clark case: the Angela Canning case and the Trupti Patel case. Roy Hill also wrote an intersting article "Reflections on the cot death cases", ''Significance'', volume 2 (2005), issue 1 in which he discusses the statistical issues in all three cases. <br />
<br />
Finding the 2000 and 2003 transcripts in Lexis Nexis.<br />
<br />
Open Lexis Nexis<br />
<br />
Choose "Legal Research" from the sidebar<br />
<br />
From "Case Law" choose "Get a Case"<br />
<br />
Choose" Commonwealth and Foreign Nations" from the sidebar<br />
<br />
Choose "Sally Clark" for the "Keyword"<br />
<br />
Choose "UK Cases" for the "Source"<br />
<br />
Choose "Previous five years” for the "Date."<br />
<br />
The two "r v Clarks" are the appeals.<br />
<br />
DISCUSSION QUESTIONS:<br />
<br />
(1) Do you think it is easonable not to allow a doctor to practice because of a statistical error in a court case?<br />
<br />
(2) Do you agree with the RSS that statistical evidence should only be provided by statistical experts?<br />
<br />
(3) Give the 73 million to 1 odds to a few of your friends and ask them if they were on the jury, in the absence of any other information, would they think that this makes it is very likely that Sally Clark is guilty?<br />
of 20 European countries from the [http:www.europeansocialsurvey.org/ the multi-nation European Social Survey ] :<br />
<br />
<center>[[Image:ForeignBorn.jpg]]</center><br />
<br />
We see that we have signficant overestimation of the number of foreign-born residents, but Germany almost got it right. You will find further discussion on this topic by Andrew and John on the July1, 2005 posting on [http://www.stat.columbia.edu/~gelman/blog/ Andrew's blog].<br />
<br />
DISCUSSION QUESTION:<br />
<br />
(1) What explanations can you think of that might explain this overestimation? Can you suggest additional research that might clarify what is going on here?<br />
<br />
== Where are recipes to be found ==<br />
People have written recipes as recipe cards, recipe books, recipes worked into needlepoint, and computer recipe databases, among others. <br />
Take notes when making your favorite dish and share your recipe in the [[list of recipes]] or Wikibooks [[Wikibooks:Cookbook|cookbook]]. <br />
<br />
The composer [[Leonard Bernstein]] set four recipes to [[music]] in his set of [[song]]s, ''La Bonne Cuisine'' (1947).<br />
<br />
== External links ==<br />
{{Cookbookpar|Recipes}}<br />
<br />
* [http://www.123cuisinez.com 123cuisinez.com - Best recipes of kitchen]<br />
*[http://www.cookbookwiki.com CookbookWiki.com] A community built Recipe Wiki. Over 20,000 recipes.<br />
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*[http://www.stratsplace.com/rogov/art_writing_recipes.html ''The Art of Writing Workable Recipes''] is a history of recipe writing, an analysis of contemporary recipe styles, and a treatise on what constitutes a well-written recipe.<br />
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*[http://www.turkishcookbook.com Binnur's Turkish Cookbook] Delicious, healthy and easy-to-make Turkish recipes.<br />
<br />
[[Category:Cooking]]<br />
<br />
[[da:Madopskrift]]<br />
[[de:Kochrezept]]<br />
[[fr:Recette]]<br />
[[ja:&#12524;&#12471;&#12500;]]<br />
[[he:&#1502;&#1514;&#1499;&#1493;&#1503;]]</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Experiment&diff=667Experiment2005-08-07T00:33:58Z<p>Laurie Snell: /* A sample Chance News */</p>
<hr />
<div>:This is an experiment to see if we can put all of Chance-News (July August) on a single page to make it easier to print it out and to make a pdf version.<br />
<br />
A '''Chance News item''' is a discription of an article in the media that uses probability or statistical concepts. <br />
<br />
A Chance News normally consist of:<br />
*The source<br />
*A discussion of the article<br />
*Discussion questions.<br />
<br />
New Chance News items and improvements to previous items are welcome for the Chance Wiki.<br />
<br />
<br />
<br />
== Quotation ==<br />
<blockquote> Numbers are like people; torture them enough and they'll tell you anything.</blockquote><br />
==Forsooth(July-Åugust 2005)<br />
Frank Duckworth, editor of the Royal Statistical Society's newsletter [http://www.therss.org.uk/publications/rssnews.html RSS NEWS] has given us permission to include items from their Forsooth column which they extract forsooth items from media sources. <br />
<br />
Of course we would be happy to have readers add items they feel are worthy of a forsooth!<br />
<br />
From the February 2005 RSS news we have:<br />
<br />
<blockquote>Glasgow's odds (on a white Christmas)<br />
had come in to 8-11, while Aberdeen<br />
was at 5-6, meaning snow in both cities<br />
is considered almost certain.</blockquote><br />
<br />
BBC website<br><br />
22 December 2004<br />
<br />
----<br />
<br />
From the May 2005 RSS News:<br />
<br />
<blockquote>He tried his best--but in the end newborn Casey-James May missed out on a 48 million-to-one record by four minutes. His father Sean, grandfather Dered and great-grandfather Alistair were all born on the same date - March 2. But Casey-James was delivered at 12.04 am on March 3....</blockquote><br />
<br />
Metro<br><br />
10 March 2005<br />
<br />
----<br />
<br />
In the US, those in the poorest households have<br />
nearly four times the risk of death of those in the richest.<br />
<br />
Your World report<br><br />
May 2004<br />
<br />
== Misperception of minorities and immigrants ==<br />
[http://www.stat.columbia.edu/~cook/movabletype/mlm/ Statistical Modeling, Causal Inference, and Social Science] is a statistics Blog. It is maintained by [http://www.stat.columbia.edu/~gelman/ Andrew Gelman], a statistician in the Departments of Statistics and Political Science at Columbia University.<br />
<br />
You will find lots of interesting statistics discussion here. Andrew also gave a [http://www.superdickery.com/stupor/2.html link] to a cartoon in which Superman shows how he would estimate the number of beans in a jar. This also qualifies as a forsooth item.<br />
<br />
In a July 1, 2005 posting Andrew continues an earlier discussion on [http://www.stat.columbia.edu/~cook/movabletype/archives/2005/06/misperception_o.html misperception of minorities]. This earlier discussion resulted from by a note from Tyler Cowen reporting that the March [http://www.harpers.org/HarpersIndex.html Harper's Index] includes the statement:<br />
<br />
<blockquote> -Average percentage of UK population that Britons believe to be immigrants: 21%<br><br />
<br />
-Actual percentage: 8%</blockquote><br />
<br />
Harpers gives as reference the Market & Opinion Research International (MORI). We could not find this statistic on the MORI website but we found something close to it in a Readers Digest (UK) report (November 2000) of a [http://www.mori.com/polls/2000/rd-july.shtml study] "Britain Today - Are We An Intolerant Nation?" that MORI did for the Readers Digest (UK) in 2000. The Digest reports:<br />
<br />
*A massive eight in ten (80%) of British adults believe that refugees come to this country because they regard Britain as 'a soft touch'.<br />
*Two thirds (66%) think that 'there are too many immigrants in Britain'.<br />
* Almost two thirds (63%) feel that 'too much is done to help immigrants'.<br />
* Nearly four in ten (37%) feel that those settling in this country 'should not maintain the culture and lifestyle they had at home'.<br />
<br />
The Digest goes on to say:<br />
<br />
* Respondents grossly overestimated the financial aid asylum seekers receive, believing on average that an asylum seeker gets £113 a week to live on. In fact, a single adult seeking asylum gets £36.54 a week in vouchers to be spent at designated stores. Just £10 may be converted to cash.<br />
* On average the public estimates that 20 per cent of the British population are immigrants. The real figure is around 4 per cent.<br />
* Similarly, they believe that on average 26 per cent of the population belong to an ethnic minority. The real figure is around 7 per cent.<br />
<br />
This last statistic is pretty close to the Harper's Index and the other responses give us some idea why they might over-estimate the percentage of immigrants.<br />
<br />
In the earlier posting, the Harper's Index comments reminded Andrew of an [http://www.washingtonpost.com/ac2/wp-dyn?pagename=article&node=&contentId=A42062-2001Jul10 article] in the Washington Post by Richard Morin (October 8, 1995) in which Morin discussed the results of a Post/Keiser/Harvard [http://www.kff.org/kaiserpolls/1105-index.cfm survey] "Four Americas: Government and Social Policy Through the Eyes of America's Multi-racial and Multi-ethnic Society"<br />
<br />
The Keiser report includes the following data:<br />
<br />
<center>[[Image:Keiser2.jpg]]</center><br />
<br />
Note that, while it is true that the White population significantly underestimated the number of African Americans, Latinos, and Asians, the same is true for each of these groups.<br />
<br />
[http://www.gwu.edu/%7Epsc/people/bio.cfm?name=sides John Sides] sent Andrew the following data on the estimated, and actual percentage of foreign-born residents in each of 20 European countries from the [http:www.europeansocialsurvey.org/ the multi-nation European Social Survey ] :<br />
<br />
<center>[[Image:ForeignBorn.jpg]]</center><br />
<br />
We see that we have signficant overestimation of the number of foreign-born residents, but Germany almost got it right. You will find further discussion on this topic by Andrew and John on the July1, 2005 posting on [http://www.stat.columbia.edu/~gelman/blog/ Andrew's blog].<br />
<br />
DISCUSSION QUESTION:<br />
<br />
(1) What explanations can you think of that might explain this overestimation? Can you suggest additional research that might clarify what is going on here?<br />
<br />
==Forsooth(JulyAugust(2002==<br />
Frank Duckworth, editor of the Royal Statistical Society's newsletter [http://www.therss.org.uk/publications/rssnews.html RSS NEWS] has given us permission to include items from their Forsooth column which they extract forsooth items from media sources. <br />
<br />
Of course we would be happy to have readers add items they feel are worthy of a forsooth!<br />
<br />
From the February 2005 RSS news we have:<br />
<br />
<blockquote>Glasgow's odds (on a white Christmas)<br />
had come in to 8-11, while Aberdeen<br />
was at 5-6, meaning snow in both cities<br />
is considered almost certain.</blockquote><br />
<br />
BBC website<br><br />
22 December 2004<br />
<br />
----<br />
<br />
From the May 2005 RSS News:<br />
<br />
<blockquote>He tried his best--but in the end newborn Casey-James May missed out on a 48 million-to-one record by four minutes. His father Sean, grandfather Dered and great-grandfather Alistair were all born on the same date - March 2. But Casey-James was delivered at 12.04 am on March 3....</blockquote><br />
<br />
Metro<br><br />
10 March 2005<br />
<br />
----<br />
<br />
In the US, those in the poorest households have<br />
nearly four times the risk of death of those in the richest.<br />
<br />
Your World report<br><br />
May 2004<br />
<br />
== A probability problem ==<br />
A Dartmouth student asked his math teacher Dana Williams if he could solve the following problem:<br />
<blockquote><br />
QUESTION: We start with n ropes and gather their 2n ends together. <br><br />
Then we randomly pair the ends and make n joins. Let E(n) <br><br />
be the expected number of loops. What is E(n)? <br />
</blockquote><br />
<br />
You might be interested in trying to solve this problem. You can check your answer [http://www.dartmouth.edu/~chance/forwiki/ropes.pdf here].<br />
<br />
DISCUSSION QUESTIONS:<br />
<br />
(1) There is probably a history to this problem. If you know a source for it please mention this on the discussion page above.<br />
<br />
(2) Can you determine the distribution of the number of loops? If not estimate this by simulation and report you results on the discussion page.<br />
<br />
== Misperception of minorities and immigrants ==<br />
[http://www.stat.columbia.edu/~cook/movabletype/mlm/ Statistical Modeling, Causal Inference, and Social Science] is a statistics Blog. It is maintained by [http://www.stat.columbia.edu/~gelman/ Andrew Gelman], a statistician in the Departments of Statistics and Political Science at Columbia University.<br />
<br />
You will find lots of interesting statistics discussion here. Andrew also gave a [http://www.superdickery.com/stupor/2.html link] to a cartoon in which Superman shows how he would estimate the number of beans in a jar. This also qualifies as a forsooth item.<br />
<br />
In a July 1, 2005 posting Andrew continues an earlier discussion on [http://www.stat.columbia.edu/~cook/movabletype/archives/2005/06/misperception_o.html misperception of minorities]. This earlier discussion resulted from by a note from Tyler Cowen reporting that the March [http://www.harpers.org/HarpersIndex.html Harper's Index] includes the statement:<br />
<br />
<blockquote> -Average percentage of UK population that Britons believe to be immigrants: 21%<br><br />
<br />
-Actual percentage: 8%</blockquote><br />
<br />
Harpers gives as reference the Market & Opinion Research International (MORI). We could not find this statistic on the MORI website but we found something close to it in a Readers Digest (UK) report (November 2000) of a [http://www.mori.com/polls/2000/rd-july.shtml study] "Britain Today - Are We An Intolerant Nation?" that MORI did for the Readers Digest (UK) in 2000. The Digest reports:<br />
<br />
*A massive eight in ten (80%) of British adults believe that refugees come to this country because they regard Britain as 'a soft touch'.<br />
*Two thirds (66%) think that 'there are too many immigrants in Britain'.<br />
* Almost two thirds (63%) feel that 'too much is done to help immigrants'.<br />
* Nearly four in ten (37%) feel that those settling in this country 'should not maintain the culture and lifestyle they had at home'.<br />
<br />
The Digest goes on to say:<br />
<br />
* Respondents grossly overestimated the financial aid asylum seekers receive, believing on average that an asylum seeker gets £113 a week to live on. In fact, a single adult seeking asylum gets £36.54 a week in vouchers to be spent at designated stores. Just £10 may be converted to cash.<br />
* On average the public estimates that 20 per cent of the British population are immigrants. The real figure is around 4 per cent.<br />
* Similarly, they believe that on average 26 per cent of the population belong to an ethnic minority. The real figure is around 7 per cent.<br />
<br />
This last statistic is pretty close to the Harper's Index and the other responses give us some idea why they might over-estimate the percentage of immigrants.<br />
<br />
In the earlier posting, the Harper's Index comments reminded Andrew of an [http://www.washingtonpost.com/ac2/wp-dyn?pagename=article&node=&contentId=A42062-2001Jul10 article] in the Washington Post by Richard Morin (October 8, 1995) in which Morin discussed the results of a Post/Keiser/Harvard [http://www.kff.org/kaiserpolls/1105-index.cfm survey] "Four Americas: Government and Social Policy Through the Eyes of America's Multi-racial and Multi-ethnic Society"<br />
<br />
The Keiser report includes the following data:<br />
<br />
<center>[[Image:Keiser2.jpg]]</center><br />
<br />
Note that, while it is true that the White population significantly underestimated the number of African Americans, Latinos, and Asians, the same is true for each of these groups.<br />
<br />
[http://www.gwu.edu/%7Epsc/people/bio.cfm?name=sides John Sides] sent Andrew the following data on the estimated, and actual percentage of foreign-born residents in each of 20 European countries from the [http:www.europeansocialsurvey.org/ the multi-nation European Social Survey ] :<br />
<br />
<center>[[Image:ForeignBorn.jpg]]</center><br />
<br />
We see that we have signficant overestimation of the number of foreign-born residents, but Germany almost got it right. You will find further discussion on this topic by Andrew and John on the July1, 2005 posting on [http://www.stat.columbia.edu/~gelman/blog/ Andrew's blog].<br />
<br />
DISCUSSION QUESTION:<br />
<br />
(1) What explanations can you think of that might explain this overestimation? Can you suggest additional research that might clarify what is going on here?<br />
<br />
== Where are recipes to be found ==<br />
People have written recipes as recipe cards, recipe books, recipes worked into needlepoint, and computer recipe databases, among others. <br />
Take notes when making your favorite dish and share your recipe in the [[list of recipes]] or Wikibooks [[Wikibooks:Cookbook|cookbook]]. <br />
<br />
The composer [[Leonard Bernstein]] set four recipes to [[music]] in his set of [[song]]s, ''La Bonne Cuisine'' (1947).<br />
<br />
== External links ==<br />
{{Cookbookpar|Recipes}}<br />
<br />
* [http://www.123cuisinez.com 123cuisinez.com - Best recipes of kitchen]<br />
*[http://www.cookbookwiki.com CookbookWiki.com] A community built Recipe Wiki. Over 20,000 recipes.<br />
*[http://www.homebasics.ca/Recipes.asp/ Homebasics Recipes] A Canadian source of fresh and delicious food ideas. 1000's of free recipes.<br />
*[http://www.allrecipes.com/ All Recipes] Over 30,000 editor-approved recipes, advanced searching abilities and rating system.<br />
*[http://www.foodgeeks.com/ ''Foodgeeks.com''] A recipe website with over 7,000 recipes.<br />
*[http://www.stratsplace.com/rogov/art_writing_recipes.html ''The Art of Writing Workable Recipes''] is a history of recipe writing, an analysis of contemporary recipe styles, and a treatise on what constitutes a well-written recipe.<br />
*[http://www.elook.org/recipes/ eLook Recipes] Over 48,000 recipes.<br />
*[http://mythunderbay.ezthemes.com/recipes/index.php Free Recipe Archive]1000's of free access Recipes<br />
*[http://www.anthus.com/Recipes/CompCook.html ''Computerized Cooking''], an analysis of recipe styles, including 14 familiar styles and some unfamiliar computer software styles. Mundie, the author, is a recipe purist who discusses what does and does not belong in a recipe.<br />
*[http://home.snafu.de/gadfly/Veggie.htm ''Veggie Life Magazine''] has published their guidelines for writing recipes. Almost all professional cooking publications have similar guidelines.<br />
*[http://sourceforge.net/projects/anymeal/ ''AnyMeal recipe database software''] is a open-source Linux-software for maintaining more than 100.000 recipes.<br />
*[http://www.visualrecipes.com ''Visual Recipes'']A community of cooks who share their recipes by taking photos of each step of the cooking process. <br />
*[http://www.foodnetwork.com/food/recipes ''Food Network Recipes'']<br />
*[http://www.bbc.co.uk/food/recipes/ ''BBC Food Recipes'']<br />
*[http://www.azpaths.com/features/diamondback-diner ''Diamondback Diner - Southwestern Recipes'']*[http://www.recipesbycathy.com ''Recipes by Cathy''] specializes in healthy but delicious cooking.<br />
*[http://www.cellartastings.com/en/food-spanish-recipes.html Spanish Recipes]<br />
*[http://www.realcajunrecipes.com/ RealCajunRecipes.com features more than 800 recipes from Cajun Country. Photos included.]<br />
*[http://www.activeangler.com/ resources/cooking offers more than 150 delicious fresh fish and seafood recipes.]<br />
*[http://welovefreebies.com/folders/Free_Recipes_and_CookBooks/ Free Recipes and Cookbooks] Directory of free recipes and cookbooks<br />
*[http://www.reciperewards.com/free 1,000's of Quick & Easy Recipes. ] The majority of the recipes have a picture. <br />
*[http://www.turkishcookbook.com Binnur's Turkish Cookbook] Delicious, healthy and easy-to-make Turkish recipes.<br />
<br />
[[Category:Cooking]]<br />
<br />
[[da:Madopskrift]]<br />
[[de:Kochrezept]]<br />
[[fr:Recette]]<br />
[[ja:&#12524;&#12471;&#12500;]]<br />
[[he:&#1502;&#1514;&#1499;&#1493;&#1503;]]</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Experiment&diff=666Experiment2005-08-07T00:27:49Z<p>Laurie Snell: </p>
<hr />
<div>:This is an experiment to see if we can put all of Chance-News (July August) on a single page to make it easier to print it out and to make a pdf version.<br />
<br />
A '''Chance News item''' is a discription of an article in the media that uses probability or statistical concepts. <br />
<br />
A Chance News normally consist of:<br />
*The source<br />
*A discussion of the article<br />
*Discussion questions.<br />
<br />
New Chance News items and improvements to previous items are welcome for the Chance Wiki.<br />
<br />
<br />
<br />
== A sample Chance News ==<br />
:''Qutation'': <br />
::<blockquote> Numbers are like people; torture them enough and they'll tell you anything.</blockquote><br />
==Forsooth(July-Åugust 2005)<br />
Frank Duckworth, editor of the Royal Statistical Society's newsletter [http://www.therss.org.uk/publications/rssnews.html RSS NEWS] has given us permission to include items from their Forsooth column which they extract forsooth items from media sources. <br />
<br />
Of course we would be happy to have readers add items they feel are worthy of a forsooth!<br />
<br />
From the February 2005 RSS news we have:<br />
<br />
<blockquote>Glasgow's odds (on a white Christmas)<br />
had come in to 8-11, while Aberdeen<br />
was at 5-6, meaning snow in both cities<br />
is considered almost certain.</blockquote><br />
<br />
BBC website<br><br />
22 December 2004<br />
<br />
----<br />
<br />
From the May 2005 RSS News:<br />
<br />
<blockquote>He tried his best--but in the end newborn Casey-James May missed out on a 48 million-to-one record by four minutes. His father Sean, grandfather Dered and great-grandfather Alistair were all born on the same date - March 2. But Casey-James was delivered at 12.04 am on March 3....</blockquote><br />
<br />
Metro<br><br />
10 March 2005<br />
<br />
----<br />
<br />
In the US, those in the poorest households have<br />
nearly four times the risk of death of those in the richest.<br />
<br />
Your World report<br><br />
May 2004<br />
<br />
==Forsooth(JulyAugust(2002==<br />
Frank Duckworth, editor of the Royal Statistical Society's newsletter [http://www.therss.org.uk/publications/rssnews.html RSS NEWS] has given us permission to include items from their Forsooth column which they extract forsooth items from media sources. <br />
<br />
Of course we would be happy to have readers add items they feel are worthy of a forsooth!<br />
<br />
From the February 2005 RSS news we have:<br />
<br />
<blockquote>Glasgow's odds (on a white Christmas)<br />
had come in to 8-11, while Aberdeen<br />
was at 5-6, meaning snow in both cities<br />
is considered almost certain.</blockquote><br />
<br />
BBC website<br><br />
22 December 2004<br />
<br />
----<br />
<br />
From the May 2005 RSS News:<br />
<br />
<blockquote>He tried his best--but in the end newborn Casey-James May missed out on a 48 million-to-one record by four minutes. His father Sean, grandfather Dered and great-grandfather Alistair were all born on the same date - March 2. But Casey-James was delivered at 12.04 am on March 3....</blockquote><br />
<br />
Metro<br><br />
10 March 2005<br />
<br />
----<br />
<br />
In the US, those in the poorest households have<br />
nearly four times the risk of death of those in the richest.<br />
<br />
Your World report<br><br />
May 2004<br />
<br />
== A probability problem ==<br />
A Dartmouth student asked his math teacher Dana Williams if he could solve the following problem:<br />
<blockquote><br />
QUESTION: We start with n ropes and gather their 2n ends together. <br><br />
Then we randomly pair the ends and make n joins. Let E(n) <br><br />
be the expected number of loops. What is E(n)? <br />
</blockquote><br />
<br />
You might be interested in trying to solve this problem. You can check your answer [http://www.dartmouth.edu/~chance/forwiki/ropes.pdf here].<br />
<br />
DISCUSSION QUESTIONS:<br />
<br />
(1) There is probably a history to this problem. If you know a source for it please mention this on the discussion page above.<br />
<br />
(2) Can you determine the distribution of the number of loops? If not estimate this by simulation and report you results on the discussion page.<br />
<br />
== Misperception of minorities and immigrants ==<br />
[http://www.stat.columbia.edu/~cook/movabletype/mlm/ Statistical Modeling, Causal Inference, and Social Science] is a statistics Blog. It is maintained by [http://www.stat.columbia.edu/~gelman/ Andrew Gelman], a statistician in the Departments of Statistics and Political Science at Columbia University.<br />
<br />
You will find lots of interesting statistics discussion here. Andrew also gave a [http://www.superdickery.com/stupor/2.html link] to a cartoon in which Superman shows how he would estimate the number of beans in a jar. This also qualifies as a forsooth item.<br />
<br />
In a July 1, 2005 posting Andrew continues an earlier discussion on [http://www.stat.columbia.edu/~cook/movabletype/archives/2005/06/misperception_o.html misperception of minorities]. This earlier discussion resulted from by a note from Tyler Cowen reporting that the March [http://www.harpers.org/HarpersIndex.html Harper's Index] includes the statement:<br />
<br />
<blockquote> -Average percentage of UK population that Britons believe to be immigrants: 21%<br><br />
<br />
-Actual percentage: 8%</blockquote><br />
<br />
Harpers gives as reference the Market & Opinion Research International (MORI). We could not find this statistic on the MORI website but we found something close to it in a Readers Digest (UK) report (November 2000) of a [http://www.mori.com/polls/2000/rd-july.shtml study] "Britain Today - Are We An Intolerant Nation?" that MORI did for the Readers Digest (UK) in 2000. The Digest reports:<br />
<br />
*A massive eight in ten (80%) of British adults believe that refugees come to this country because they regard Britain as 'a soft touch'.<br />
*Two thirds (66%) think that 'there are too many immigrants in Britain'.<br />
* Almost two thirds (63%) feel that 'too much is done to help immigrants'.<br />
* Nearly four in ten (37%) feel that those settling in this country 'should not maintain the culture and lifestyle they had at home'.<br />
<br />
The Digest goes on to say:<br />
<br />
* Respondents grossly overestimated the financial aid asylum seekers receive, believing on average that an asylum seeker gets £113 a week to live on. In fact, a single adult seeking asylum gets £36.54 a week in vouchers to be spent at designated stores. Just £10 may be converted to cash.<br />
* On average the public estimates that 20 per cent of the British population are immigrants. The real figure is around 4 per cent.<br />
* Similarly, they believe that on average 26 per cent of the population belong to an ethnic minority. The real figure is around 7 per cent.<br />
<br />
This last statistic is pretty close to the Harper's Index and the other responses give us some idea why they might over-estimate the percentage of immigrants.<br />
<br />
In the earlier posting, the Harper's Index comments reminded Andrew of an [http://www.washingtonpost.com/ac2/wp-dyn?pagename=article&node=&contentId=A42062-2001Jul10 article] in the Washington Post by Richard Morin (October 8, 1995) in which Morin discussed the results of a Post/Keiser/Harvard [http://www.kff.org/kaiserpolls/1105-index.cfm survey] "Four Americas: Government and Social Policy Through the Eyes of America's Multi-racial and Multi-ethnic Society"<br />
<br />
The Keiser report includes the following data:<br />
<br />
<center>[[Image:Keiser2.jpg]]</center><br />
<br />
Note that, while it is true that the White population significantly underestimated the number of African Americans, Latinos, and Asians, the same is true for each of these groups.<br />
<br />
[http://www.gwu.edu/%7Epsc/people/bio.cfm?name=sides John Sides] sent Andrew the following data on the estimated, and actual percentage of foreign-born residents in each of 20 European countries from the [http:www.europeansocialsurvey.org/ the multi-nation European Social Survey ] :<br />
<br />
<center>[[Image:ForeignBorn.jpg]]</center><br />
<br />
We see that we have signficant overestimation of the number of foreign-born residents, but Germany almost got it right. You will find further discussion on this topic by Andrew and John on the July1, 2005 posting on [http://www.stat.columbia.edu/~gelman/blog/ Andrew's blog].<br />
<br />
DISCUSSION QUESTION:<br />
<br />
(1) What explanations can you think of that might explain this overestimation? Can you suggest additional research that might clarify what is going on here?<br />
<br />
== Where are recipes to be found ==<br />
People have written recipes as recipe cards, recipe books, recipes worked into needlepoint, and computer recipe databases, among others. <br />
Take notes when making your favorite dish and share your recipe in the [[list of recipes]] or Wikibooks [[Wikibooks:Cookbook|cookbook]]. <br />
<br />
The composer [[Leonard Bernstein]] set four recipes to [[music]] in his set of [[song]]s, ''La Bonne Cuisine'' (1947).<br />
<br />
== External links ==<br />
{{Cookbookpar|Recipes}}<br />
<br />
* [http://www.123cuisinez.com 123cuisinez.com - Best recipes of kitchen]<br />
*[http://www.cookbookwiki.com CookbookWiki.com] A community built Recipe Wiki. Over 20,000 recipes.<br />
*[http://www.homebasics.ca/Recipes.asp/ Homebasics Recipes] A Canadian source of fresh and delicious food ideas. 1000's of free recipes.<br />
*[http://www.allrecipes.com/ All Recipes] Over 30,000 editor-approved recipes, advanced searching abilities and rating system.<br />
*[http://www.foodgeeks.com/ ''Foodgeeks.com''] A recipe website with over 7,000 recipes.<br />
*[http://www.stratsplace.com/rogov/art_writing_recipes.html ''The Art of Writing Workable Recipes''] is a history of recipe writing, an analysis of contemporary recipe styles, and a treatise on what constitutes a well-written recipe.<br />
*[http://www.elook.org/recipes/ eLook Recipes] Over 48,000 recipes.<br />
*[http://mythunderbay.ezthemes.com/recipes/index.php Free Recipe Archive]1000's of free access Recipes<br />
*[http://www.anthus.com/Recipes/CompCook.html ''Computerized Cooking''], an analysis of recipe styles, including 14 familiar styles and some unfamiliar computer software styles. Mundie, the author, is a recipe purist who discusses what does and does not belong in a recipe.<br />
*[http://home.snafu.de/gadfly/Veggie.htm ''Veggie Life Magazine''] has published their guidelines for writing recipes. Almost all professional cooking publications have similar guidelines.<br />
*[http://sourceforge.net/projects/anymeal/ ''AnyMeal recipe database software''] is a open-source Linux-software for maintaining more than 100.000 recipes.<br />
*[http://www.visualrecipes.com ''Visual Recipes'']A community of cooks who share their recipes by taking photos of each step of the cooking process. <br />
*[http://www.foodnetwork.com/food/recipes ''Food Network Recipes'']<br />
*[http://www.bbc.co.uk/food/recipes/ ''BBC Food Recipes'']<br />
*[http://www.azpaths.com/features/diamondback-diner ''Diamondback Diner - Southwestern Recipes'']*[http://www.recipesbycathy.com ''Recipes by Cathy''] specializes in healthy but delicious cooking.<br />
*[http://www.cellartastings.com/en/food-spanish-recipes.html Spanish Recipes]<br />
*[http://www.realcajunrecipes.com/ RealCajunRecipes.com features more than 800 recipes from Cajun Country. Photos included.]<br />
*[http://www.activeangler.com/ resources/cooking offers more than 150 delicious fresh fish and seafood recipes.]<br />
*[http://welovefreebies.com/folders/Free_Recipes_and_CookBooks/ Free Recipes and Cookbooks] Directory of free recipes and cookbooks<br />
*[http://www.reciperewards.com/free 1,000's of Quick & Easy Recipes. ] The majority of the recipes have a picture. <br />
*[http://www.turkishcookbook.com Binnur's Turkish Cookbook] Delicious, healthy and easy-to-make Turkish recipes.<br />
<br />
[[Category:Cooking]]<br />
<br />
[[da:Madopskrift]]<br />
[[de:Kochrezept]]<br />
[[fr:Recette]]<br />
[[ja:&#12524;&#12471;&#12500;]]<br />
[[he:&#1502;&#1514;&#1499;&#1493;&#1503;]]</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Experiment&diff=665Experiment2005-08-07T00:21:44Z<p>Laurie Snell: /* What else might be included */</p>
<hr />
<div>:This is an experiment to see if we can put all of Chance-News (July August) on a single page to make it easier to print it out and to make a pdf version.<br />
<br />
A '''Chance News item''' is a discription of an article in the media that uses probability or statistical concepts. <br />
<br />
A Chance News normally consist of:<br />
*The source<br />
*A discussion of the article<br />
*Discussion questions.<br />
<br />
New Chance News items and improvements to previous items are welcome for the Chance Wiki.<br />
<br />
<br />
<br />
== A sample Chance News ==<br />
:''Qutation'': <br />
::<blockquote> Numbers are like people; torture them enough and they'll tell you anything.</blockquote><br />
==Forsooth(July-Åugust 2005)<br />
Frank Duckworth, editor of the Royal Statistical Society's newsletter [http://www.therss.org.uk/publications/rssnews.html RSS NEWS] has given us permission to include items from their Forsooth column which they extract forsooth items from media sources. <br />
<br />
Of course we would be happy to have readers add items they feel are worthy of a forsooth!<br />
<br />
From the February 2005 RSS news we have:<br />
<br />
<blockquote>Glasgow's odds (on a white Christmas)<br />
had come in to 8-11, while Aberdeen<br />
was at 5-6, meaning snow in both cities<br />
is considered almost certain.</blockquote><br />
<br />
BBC website<br><br />
22 December 2004<br />
<br />
----<br />
<br />
From the May 2005 RSS News:<br />
<br />
<blockquote>He tried his best--but in the end newborn Casey-James May missed out on a 48 million-to-one record by four minutes. His father Sean, grandfather Dered and great-grandfather Alistair were all born on the same date - March 2. But Casey-James was delivered at 12.04 am on March 3....</blockquote><br />
<br />
Metro<br><br />
10 March 2005<br />
<br />
----<br />
<br />
In the US, those in the poorest households have<br />
nearly four times the risk of death of those in the richest.<br />
<br />
Your World report<br><br />
May 2004<br />
<br />
==Forsooth(JulyAugust(2002==<br />
Frank Duckworth, editor of the Royal Statistical Society's newsletter [http://www.therss.org.uk/publications/rssnews.html RSS NEWS] has given us permission to include items from their Forsooth column which they extract forsooth items from media sources. <br />
<br />
Of course we would be happy to have readers add items they feel are worthy of a forsooth!<br />
<br />
From the February 2005 RSS news we have:<br />
<br />
<blockquote>Glasgow's odds (on a white Christmas)<br />
had come in to 8-11, while Aberdeen<br />
was at 5-6, meaning snow in both cities<br />
is considered almost certain.</blockquote><br />
<br />
BBC website<br><br />
22 December 2004<br />
<br />
----<br />
<br />
From the May 2005 RSS News:<br />
<br />
<blockquote>He tried his best--but in the end newborn Casey-James May missed out on a 48 million-to-one record by four minutes. His father Sean, grandfather Dered and great-grandfather Alistair were all born on the same date - March 2. But Casey-James was delivered at 12.04 am on March 3....</blockquote><br />
<br />
Metro<br><br />
10 March 2005<br />
<br />
----<br />
<br />
In the US, those in the poorest households have<br />
nearly four times the risk of death of those in the richest.<br />
<br />
Your World report<br><br />
May 2004<br />
<br />
== A probability problem ==<br />
A Dartmouth student asked his math teacher Dana Williams if he could solve the following problem:<br />
<blockquote><br />
QUESTION: We start with n ropes and gather their 2n ends together. <br><br />
Then we randomly pair the ends and make n joins. Let E(n) <br><br />
be the expected number of loops. What is E(n)? <br />
</blockquote><br />
<br />
You might be interested in trying to solve this problem. You can check your answer [http://www.dartmouth.edu/~chance/forwiki/ropes.pdf here].<br />
<br />
DISCUSSION QUESTIONS:<br />
<br />
(1) There is probably a history to this problem. If you know a source for it please mention this on the discussion page above.<br />
<br />
(2) Can you determine the distribution of the number of loops? If not estimate this by simulation and report you results on the discussion page.<br />
<br />
== Additional facts often included in recipes ==<br />
Recipe writers often add additional facts about the recipe, and, depending upon who you are, they are considered redundant or essential.<br />
<br />
Such facts may include the history of the dish, nutritional information, dietary information, philosophical ramblings about the soul-enriching or health-benefiting properties of the dish, or what wonderful hostess in what particular town first served the dish to the author.<br />
<br />
Nutritional information normally includes [[food energy]], vitamin content, fat content, etc.<br />
<br />
== Where are recipes to be found ==<br />
People have written recipes as recipe cards, recipe books, recipes worked into needlepoint, and computer recipe databases, among others. <br />
Take notes when making your favorite dish and share your recipe in the [[list of recipes]] or Wikibooks [[Wikibooks:Cookbook|cookbook]]. <br />
<br />
The composer [[Leonard Bernstein]] set four recipes to [[music]] in his set of [[song]]s, ''La Bonne Cuisine'' (1947).<br />
<br />
== External links ==<br />
{{Cookbookpar|Recipes}}<br />
<br />
* [http://www.123cuisinez.com 123cuisinez.com - Best recipes of kitchen]<br />
*[http://www.cookbookwiki.com CookbookWiki.com] A community built Recipe Wiki. Over 20,000 recipes.<br />
*[http://www.homebasics.ca/Recipes.asp/ Homebasics Recipes] A Canadian source of fresh and delicious food ideas. 1000's of free recipes.<br />
*[http://www.allrecipes.com/ All Recipes] Over 30,000 editor-approved recipes, advanced searching abilities and rating system.<br />
*[http://www.foodgeeks.com/ ''Foodgeeks.com''] A recipe website with over 7,000 recipes.<br />
*[http://www.stratsplace.com/rogov/art_writing_recipes.html ''The Art of Writing Workable Recipes''] is a history of recipe writing, an analysis of contemporary recipe styles, and a treatise on what constitutes a well-written recipe.<br />
*[http://www.elook.org/recipes/ eLook Recipes] Over 48,000 recipes.<br />
*[http://mythunderbay.ezthemes.com/recipes/index.php Free Recipe Archive]1000's of free access Recipes<br />
*[http://www.anthus.com/Recipes/CompCook.html ''Computerized Cooking''], an analysis of recipe styles, including 14 familiar styles and some unfamiliar computer software styles. Mundie, the author, is a recipe purist who discusses what does and does not belong in a recipe.<br />
*[http://home.snafu.de/gadfly/Veggie.htm ''Veggie Life Magazine''] has published their guidelines for writing recipes. Almost all professional cooking publications have similar guidelines.<br />
*[http://sourceforge.net/projects/anymeal/ ''AnyMeal recipe database software''] is a open-source Linux-software for maintaining more than 100.000 recipes.<br />
*[http://www.visualrecipes.com ''Visual Recipes'']A community of cooks who share their recipes by taking photos of each step of the cooking process. <br />
*[http://www.foodnetwork.com/food/recipes ''Food Network Recipes'']<br />
*[http://www.bbc.co.uk/food/recipes/ ''BBC Food Recipes'']<br />
*[http://www.azpaths.com/features/diamondback-diner ''Diamondback Diner - Southwestern Recipes'']*[http://www.recipesbycathy.com ''Recipes by Cathy''] specializes in healthy but delicious cooking.<br />
*[http://www.cellartastings.com/en/food-spanish-recipes.html Spanish Recipes]<br />
*[http://www.realcajunrecipes.com/ RealCajunRecipes.com features more than 800 recipes from Cajun Country. Photos included.]<br />
*[http://www.activeangler.com/ resources/cooking offers more than 150 delicious fresh fish and seafood recipes.]<br />
*[http://welovefreebies.com/folders/Free_Recipes_and_CookBooks/ Free Recipes and Cookbooks] Directory of free recipes and cookbooks<br />
*[http://www.reciperewards.com/free 1,000's of Quick & Easy Recipes. ] The majority of the recipes have a picture. <br />
*[http://www.turkishcookbook.com Binnur's Turkish Cookbook] Delicious, healthy and easy-to-make Turkish recipes.<br />
<br />
[[Category:Cooking]]<br />
<br />
[[da:Madopskrift]]<br />
[[de:Kochrezept]]<br />
[[fr:Recette]]<br />
[[ja:&#12524;&#12471;&#12500;]]<br />
[[he:&#1502;&#1514;&#1499;&#1493;&#1503;]]</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Experiment&diff=664Experiment2005-08-07T00:19:08Z<p>Laurie Snell: /* Forsooth(JulyAugust(2002) */</p>
<hr />
<div>:This is an experiment to see if we can put all of Chance-News (July August) on a single page to make it easier to print it out and to make a pdf version.<br />
<br />
A '''Chance News item''' is a discription of an article in the media that uses probability or statistical concepts. <br />
<br />
A Chance News normally consist of:<br />
*The source<br />
*A discussion of the article<br />
*Discussion questions.<br />
<br />
New Chance News items and improvements to previous items are welcome for the Chance Wiki.<br />
<br />
<br />
<br />
== A sample Chance News ==<br />
:''Qutation'': <br />
::<blockquote> Numbers are like people; torture them enough and they'll tell you anything.</blockquote><br />
==Forsooth(July-Åugust 2005)<br />
Frank Duckworth, editor of the Royal Statistical Society's newsletter [http://www.therss.org.uk/publications/rssnews.html RSS NEWS] has given us permission to include items from their Forsooth column which they extract forsooth items from media sources. <br />
<br />
Of course we would be happy to have readers add items they feel are worthy of a forsooth!<br />
<br />
From the February 2005 RSS news we have:<br />
<br />
<blockquote>Glasgow's odds (on a white Christmas)<br />
had come in to 8-11, while Aberdeen<br />
was at 5-6, meaning snow in both cities<br />
is considered almost certain.</blockquote><br />
<br />
BBC website<br><br />
22 December 2004<br />
<br />
----<br />
<br />
From the May 2005 RSS News:<br />
<br />
<blockquote>He tried his best--but in the end newborn Casey-James May missed out on a 48 million-to-one record by four minutes. His father Sean, grandfather Dered and great-grandfather Alistair were all born on the same date - March 2. But Casey-James was delivered at 12.04 am on March 3....</blockquote><br />
<br />
Metro<br><br />
10 March 2005<br />
<br />
----<br />
<br />
In the US, those in the poorest households have<br />
nearly four times the risk of death of those in the richest.<br />
<br />
Your World report<br><br />
May 2004<br />
<br />
==Forsooth(JulyAugust(2002==<br />
Frank Duckworth, editor of the Royal Statistical Society's newsletter [http://www.therss.org.uk/publications/rssnews.html RSS NEWS] has given us permission to include items from their Forsooth column which they extract forsooth items from media sources. <br />
<br />
Of course we would be happy to have readers add items they feel are worthy of a forsooth!<br />
<br />
From the February 2005 RSS news we have:<br />
<br />
<blockquote>Glasgow's odds (on a white Christmas)<br />
had come in to 8-11, while Aberdeen<br />
was at 5-6, meaning snow in both cities<br />
is considered almost certain.</blockquote><br />
<br />
BBC website<br><br />
22 December 2004<br />
<br />
----<br />
<br />
From the May 2005 RSS News:<br />
<br />
<blockquote>He tried his best--but in the end newborn Casey-James May missed out on a 48 million-to-one record by four minutes. His father Sean, grandfather Dered and great-grandfather Alistair were all born on the same date - March 2. But Casey-James was delivered at 12.04 am on March 3....</blockquote><br />
<br />
Metro<br><br />
10 March 2005<br />
<br />
----<br />
<br />
In the US, those in the poorest households have<br />
nearly four times the risk of death of those in the richest.<br />
<br />
Your World report<br><br />
May 2004<br />
<br />
== What else might be included ==<br />
*Special handling requirements (how are eggs or butter stored? At what temperature should they be when cooking starts?)<br />
*Garnishing or serving advice (add a sprig of parsley for color).<br />
<br />
== Additional facts often included in recipes ==<br />
Recipe writers often add additional facts about the recipe, and, depending upon who you are, they are considered redundant or essential.<br />
<br />
Such facts may include the history of the dish, nutritional information, dietary information, philosophical ramblings about the soul-enriching or health-benefiting properties of the dish, or what wonderful hostess in what particular town first served the dish to the author.<br />
<br />
Nutritional information normally includes [[food energy]], vitamin content, fat content, etc.<br />
<br />
== Where are recipes to be found ==<br />
People have written recipes as recipe cards, recipe books, recipes worked into needlepoint, and computer recipe databases, among others. <br />
Take notes when making your favorite dish and share your recipe in the [[list of recipes]] or Wikibooks [[Wikibooks:Cookbook|cookbook]]. <br />
<br />
The composer [[Leonard Bernstein]] set four recipes to [[music]] in his set of [[song]]s, ''La Bonne Cuisine'' (1947).<br />
<br />
== External links ==<br />
{{Cookbookpar|Recipes}}<br />
<br />
* [http://www.123cuisinez.com 123cuisinez.com - Best recipes of kitchen]<br />
*[http://www.cookbookwiki.com CookbookWiki.com] A community built Recipe Wiki. Over 20,000 recipes.<br />
*[http://www.homebasics.ca/Recipes.asp/ Homebasics Recipes] A Canadian source of fresh and delicious food ideas. 1000's of free recipes.<br />
*[http://www.allrecipes.com/ All Recipes] Over 30,000 editor-approved recipes, advanced searching abilities and rating system.<br />
*[http://www.foodgeeks.com/ ''Foodgeeks.com''] A recipe website with over 7,000 recipes.<br />
*[http://www.stratsplace.com/rogov/art_writing_recipes.html ''The Art of Writing Workable Recipes''] is a history of recipe writing, an analysis of contemporary recipe styles, and a treatise on what constitutes a well-written recipe.<br />
*[http://www.elook.org/recipes/ eLook Recipes] Over 48,000 recipes.<br />
*[http://mythunderbay.ezthemes.com/recipes/index.php Free Recipe Archive]1000's of free access Recipes<br />
*[http://www.anthus.com/Recipes/CompCook.html ''Computerized Cooking''], an analysis of recipe styles, including 14 familiar styles and some unfamiliar computer software styles. Mundie, the author, is a recipe purist who discusses what does and does not belong in a recipe.<br />
*[http://home.snafu.de/gadfly/Veggie.htm ''Veggie Life Magazine''] has published their guidelines for writing recipes. Almost all professional cooking publications have similar guidelines.<br />
*[http://sourceforge.net/projects/anymeal/ ''AnyMeal recipe database software''] is a open-source Linux-software for maintaining more than 100.000 recipes.<br />
*[http://www.visualrecipes.com ''Visual Recipes'']A community of cooks who share their recipes by taking photos of each step of the cooking process. <br />
*[http://www.foodnetwork.com/food/recipes ''Food Network Recipes'']<br />
*[http://www.bbc.co.uk/food/recipes/ ''BBC Food Recipes'']<br />
*[http://www.azpaths.com/features/diamondback-diner ''Diamondback Diner - Southwestern Recipes'']*[http://www.recipesbycathy.com ''Recipes by Cathy''] specializes in healthy but delicious cooking.<br />
*[http://www.cellartastings.com/en/food-spanish-recipes.html Spanish Recipes]<br />
*[http://www.realcajunrecipes.com/ RealCajunRecipes.com features more than 800 recipes from Cajun Country. Photos included.]<br />
*[http://www.activeangler.com/ resources/cooking offers more than 150 delicious fresh fish and seafood recipes.]<br />
*[http://welovefreebies.com/folders/Free_Recipes_and_CookBooks/ Free Recipes and Cookbooks] Directory of free recipes and cookbooks<br />
*[http://www.reciperewards.com/free 1,000's of Quick & Easy Recipes. ] The majority of the recipes have a picture. <br />
*[http://www.turkishcookbook.com Binnur's Turkish Cookbook] Delicious, healthy and easy-to-make Turkish recipes.<br />
<br />
[[Category:Cooking]]<br />
<br />
[[da:Madopskrift]]<br />
[[de:Kochrezept]]<br />
[[fr:Recette]]<br />
[[ja:&#12524;&#12471;&#12500;]]<br />
[[he:&#1502;&#1514;&#1499;&#1493;&#1503;]]</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Experiment&diff=663Experiment2005-08-07T00:17:34Z<p>Laurie Snell: /* A sample Chance News */</p>
<hr />
<div>:This is an experiment to see if we can put all of Chance-News (July August) on a single page to make it easier to print it out and to make a pdf version.<br />
<br />
A '''Chance News item''' is a discription of an article in the media that uses probability or statistical concepts. <br />
<br />
A Chance News normally consist of:<br />
*The source<br />
*A discussion of the article<br />
*Discussion questions.<br />
<br />
New Chance News items and improvements to previous items are welcome for the Chance Wiki.<br />
<br />
<br />
<br />
== A sample Chance News ==<br />
:''Qutation'': <br />
::<blockquote> Numbers are like people; torture them enough and they'll tell you anything.</blockquote><br />
==Forsooth(July-Åugust 2005)<br />
Frank Duckworth, editor of the Royal Statistical Society's newsletter [http://www.therss.org.uk/publications/rssnews.html RSS NEWS] has given us permission to include items from their Forsooth column which they extract forsooth items from media sources. <br />
<br />
Of course we would be happy to have readers add items they feel are worthy of a forsooth!<br />
<br />
From the February 2005 RSS news we have:<br />
<br />
<blockquote>Glasgow's odds (on a white Christmas)<br />
had come in to 8-11, while Aberdeen<br />
was at 5-6, meaning snow in both cities<br />
is considered almost certain.</blockquote><br />
<br />
BBC website<br><br />
22 December 2004<br />
<br />
----<br />
<br />
From the May 2005 RSS News:<br />
<br />
<blockquote>He tried his best--but in the end newborn Casey-James May missed out on a 48 million-to-one record by four minutes. His father Sean, grandfather Dered and great-grandfather Alistair were all born on the same date - March 2. But Casey-James was delivered at 12.04 am on March 3....</blockquote><br />
<br />
Metro<br><br />
10 March 2005<br />
<br />
----<br />
<br />
In the US, those in the poorest households have<br />
nearly four times the risk of death of those in the richest.<br />
<br />
Your World report<br><br />
May 2004<br />
<br />
==Forsooth(JulyAugust(2002)==<br />
Frank Duckworth, editor of the Royal Statistical Society's newsletter [http://www.therss.org.uk/publications/rssnews.html RSS NEWS] has given us permission to include items from their Forsooth column which they extract forsooth items from media sources. <br />
<br />
Of course we would be happy to have readers add items they feel are worthy of a forsooth!<br />
<br />
From the February 2005 RSS news we have:<br />
<br />
<blockquote>Glasgow's odds (on a white Christmas)<br />
had come in to 8-11, while Aberdeen<br />
was at 5-6, meaning snow in both cities<br />
is considered almost certain.</blockquote><br />
<br />
BBC website<br><br />
22 December 2004<br />
<br />
----<br />
<br />
From the May 2005 RSS News:<br />
<br />
<blockquote>He tried his best--but in the end newborn Casey-James May missed out on a 48 million-to-one record by four minutes. His father Sean, grandfather Dered and great-grandfather Alistair were all born on the same date - March 2. But Casey-James was delivered at 12.04 am on March 3....</blockquote><br />
<br />
Metro<br><br />
10 March 2005<br />
<br />
----<br />
<br />
In the US, those in the poorest households have<br />
nearly four times the risk of death of those in the richest.<br />
<br />
Your World report<br><br />
May 2004<br />
<br />
== What else might be included ==<br />
*Special handling requirements (how are eggs or butter stored? At what temperature should they be when cooking starts?)<br />
*Garnishing or serving advice (add a sprig of parsley for color).<br />
<br />
== Additional facts often included in recipes ==<br />
Recipe writers often add additional facts about the recipe, and, depending upon who you are, they are considered redundant or essential.<br />
<br />
Such facts may include the history of the dish, nutritional information, dietary information, philosophical ramblings about the soul-enriching or health-benefiting properties of the dish, or what wonderful hostess in what particular town first served the dish to the author.<br />
<br />
Nutritional information normally includes [[food energy]], vitamin content, fat content, etc.<br />
<br />
== Where are recipes to be found ==<br />
People have written recipes as recipe cards, recipe books, recipes worked into needlepoint, and computer recipe databases, among others. <br />
Take notes when making your favorite dish and share your recipe in the [[list of recipes]] or Wikibooks [[Wikibooks:Cookbook|cookbook]]. <br />
<br />
The composer [[Leonard Bernstein]] set four recipes to [[music]] in his set of [[song]]s, ''La Bonne Cuisine'' (1947).<br />
<br />
== External links ==<br />
{{Cookbookpar|Recipes}}<br />
<br />
* [http://www.123cuisinez.com 123cuisinez.com - Best recipes of kitchen]<br />
*[http://www.cookbookwiki.com CookbookWiki.com] A community built Recipe Wiki. Over 20,000 recipes.<br />
*[http://www.homebasics.ca/Recipes.asp/ Homebasics Recipes] A Canadian source of fresh and delicious food ideas. 1000's of free recipes.<br />
*[http://www.allrecipes.com/ All Recipes] Over 30,000 editor-approved recipes, advanced searching abilities and rating system.<br />
*[http://www.foodgeeks.com/ ''Foodgeeks.com''] A recipe website with over 7,000 recipes.<br />
*[http://www.stratsplace.com/rogov/art_writing_recipes.html ''The Art of Writing Workable Recipes''] is a history of recipe writing, an analysis of contemporary recipe styles, and a treatise on what constitutes a well-written recipe.<br />
*[http://www.elook.org/recipes/ eLook Recipes] Over 48,000 recipes.<br />
*[http://mythunderbay.ezthemes.com/recipes/index.php Free Recipe Archive]1000's of free access Recipes<br />
*[http://www.anthus.com/Recipes/CompCook.html ''Computerized Cooking''], an analysis of recipe styles, including 14 familiar styles and some unfamiliar computer software styles. Mundie, the author, is a recipe purist who discusses what does and does not belong in a recipe.<br />
*[http://home.snafu.de/gadfly/Veggie.htm ''Veggie Life Magazine''] has published their guidelines for writing recipes. Almost all professional cooking publications have similar guidelines.<br />
*[http://sourceforge.net/projects/anymeal/ ''AnyMeal recipe database software''] is a open-source Linux-software for maintaining more than 100.000 recipes.<br />
*[http://www.visualrecipes.com ''Visual Recipes'']A community of cooks who share their recipes by taking photos of each step of the cooking process. <br />
*[http://www.foodnetwork.com/food/recipes ''Food Network Recipes'']<br />
*[http://www.bbc.co.uk/food/recipes/ ''BBC Food Recipes'']<br />
*[http://www.azpaths.com/features/diamondback-diner ''Diamondback Diner - Southwestern Recipes'']*[http://www.recipesbycathy.com ''Recipes by Cathy''] specializes in healthy but delicious cooking.<br />
*[http://www.cellartastings.com/en/food-spanish-recipes.html Spanish Recipes]<br />
*[http://www.realcajunrecipes.com/ RealCajunRecipes.com features more than 800 recipes from Cajun Country. Photos included.]<br />
*[http://www.activeangler.com/ resources/cooking offers more than 150 delicious fresh fish and seafood recipes.]<br />
*[http://welovefreebies.com/folders/Free_Recipes_and_CookBooks/ Free Recipes and Cookbooks] Directory of free recipes and cookbooks<br />
*[http://www.reciperewards.com/free 1,000's of Quick & Easy Recipes. ] The majority of the recipes have a picture. <br />
*[http://www.turkishcookbook.com Binnur's Turkish Cookbook] Delicious, healthy and easy-to-make Turkish recipes.<br />
<br />
[[Category:Cooking]]<br />
<br />
[[da:Madopskrift]]<br />
[[de:Kochrezept]]<br />
[[fr:Recette]]<br />
[[ja:&#12524;&#12471;&#12500;]]<br />
[[he:&#1502;&#1514;&#1499;&#1493;&#1503;]]</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Experiment&diff=662Experiment2005-08-07T00:13:05Z<p>Laurie Snell: </p>
<hr />
<div>:This is an experiment to see if we can put all of Chance-News (July August) on a single page to make it easier to print it out and to make a pdf version.<br />
<br />
A '''Chance News item''' is a discription of an article in the media that uses probability or statistical concepts. <br />
<br />
A Chance News normally consist of:<br />
*The source<br />
*A discussion of the article<br />
*Discussion questions.<br />
<br />
New Chance News items and improvements to previous items are welcome for the Chance Wiki.<br />
<br />
<br />
<br />
== A sample Chance News ==<br />
:''Qutation'': <br />
::<blockquote> Numbers are like people; torture them enough and they'll tell you anything.</blockquote><br />
==Forsooth(JulyAugust(2002)==<br />
Frank Duckworth, editor of the Royal Statistical Society's newsletter [http://www.therss.org.uk/publications/rssnews.html RSS NEWS] has given us permission to include items from their Forsooth column which they extract forsooth items from media sources. <br />
<br />
Of course we would be happy to have readers add items they feel are worthy of a forsooth!<br />
<br />
From the February 2005 RSS news we have:<br />
<br />
<blockquote>Glasgow's odds (on a white Christmas)<br />
had come in to 8-11, while Aberdeen<br />
was at 5-6, meaning snow in both cities<br />
is considered almost certain.</blockquote><br />
<br />
BBC website<br><br />
22 December 2004<br />
<br />
----<br />
<br />
From the May 2005 RSS News:<br />
<br />
<blockquote>He tried his best--but in the end newborn Casey-James May missed out on a 48 million-to-one record by four minutes. His father Sean, grandfather Dered and great-grandfather Alistair were all born on the same date - March 2. But Casey-James was delivered at 12.04 am on March 3....</blockquote><br />
<br />
Metro<br><br />
10 March 2005<br />
<br />
----<br />
<br />
In the US, those in the poorest households have<br />
nearly four times the risk of death of those in the richest.<br />
<br />
Your World report<br><br />
May 2004<br />
<br />
== What else might be included ==<br />
*Special handling requirements (how are eggs or butter stored? At what temperature should they be when cooking starts?)<br />
*Garnishing or serving advice (add a sprig of parsley for color).<br />
<br />
== Additional facts often included in recipes ==<br />
Recipe writers often add additional facts about the recipe, and, depending upon who you are, they are considered redundant or essential.<br />
<br />
Such facts may include the history of the dish, nutritional information, dietary information, philosophical ramblings about the soul-enriching or health-benefiting properties of the dish, or what wonderful hostess in what particular town first served the dish to the author.<br />
<br />
Nutritional information normally includes [[food energy]], vitamin content, fat content, etc.<br />
<br />
== Where are recipes to be found ==<br />
People have written recipes as recipe cards, recipe books, recipes worked into needlepoint, and computer recipe databases, among others. <br />
Take notes when making your favorite dish and share your recipe in the [[list of recipes]] or Wikibooks [[Wikibooks:Cookbook|cookbook]]. <br />
<br />
The composer [[Leonard Bernstein]] set four recipes to [[music]] in his set of [[song]]s, ''La Bonne Cuisine'' (1947).<br />
<br />
== External links ==<br />
{{Cookbookpar|Recipes}}<br />
<br />
* [http://www.123cuisinez.com 123cuisinez.com - Best recipes of kitchen]<br />
*[http://www.cookbookwiki.com CookbookWiki.com] A community built Recipe Wiki. Over 20,000 recipes.<br />
*[http://www.homebasics.ca/Recipes.asp/ Homebasics Recipes] A Canadian source of fresh and delicious food ideas. 1000's of free recipes.<br />
*[http://www.allrecipes.com/ All Recipes] Over 30,000 editor-approved recipes, advanced searching abilities and rating system.<br />
*[http://www.foodgeeks.com/ ''Foodgeeks.com''] A recipe website with over 7,000 recipes.<br />
*[http://www.stratsplace.com/rogov/art_writing_recipes.html ''The Art of Writing Workable Recipes''] is a history of recipe writing, an analysis of contemporary recipe styles, and a treatise on what constitutes a well-written recipe.<br />
*[http://www.elook.org/recipes/ eLook Recipes] Over 48,000 recipes.<br />
*[http://mythunderbay.ezthemes.com/recipes/index.php Free Recipe Archive]1000's of free access Recipes<br />
*[http://www.anthus.com/Recipes/CompCook.html ''Computerized Cooking''], an analysis of recipe styles, including 14 familiar styles and some unfamiliar computer software styles. Mundie, the author, is a recipe purist who discusses what does and does not belong in a recipe.<br />
*[http://home.snafu.de/gadfly/Veggie.htm ''Veggie Life Magazine''] has published their guidelines for writing recipes. Almost all professional cooking publications have similar guidelines.<br />
*[http://sourceforge.net/projects/anymeal/ ''AnyMeal recipe database software''] is a open-source Linux-software for maintaining more than 100.000 recipes.<br />
*[http://www.visualrecipes.com ''Visual Recipes'']A community of cooks who share their recipes by taking photos of each step of the cooking process. <br />
*[http://www.foodnetwork.com/food/recipes ''Food Network Recipes'']<br />
*[http://www.bbc.co.uk/food/recipes/ ''BBC Food Recipes'']<br />
*[http://www.azpaths.com/features/diamondback-diner ''Diamondback Diner - Southwestern Recipes'']*[http://www.recipesbycathy.com ''Recipes by Cathy''] specializes in healthy but delicious cooking.<br />
*[http://www.cellartastings.com/en/food-spanish-recipes.html Spanish Recipes]<br />
*[http://www.realcajunrecipes.com/ RealCajunRecipes.com features more than 800 recipes from Cajun Country. Photos included.]<br />
*[http://www.activeangler.com/ resources/cooking offers more than 150 delicious fresh fish and seafood recipes.]<br />
*[http://welovefreebies.com/folders/Free_Recipes_and_CookBooks/ Free Recipes and Cookbooks] Directory of free recipes and cookbooks<br />
*[http://www.reciperewards.com/free 1,000's of Quick & Easy Recipes. ] The majority of the recipes have a picture. <br />
*[http://www.turkishcookbook.com Binnur's Turkish Cookbook] Delicious, healthy and easy-to-make Turkish recipes.<br />
<br />
[[Category:Cooking]]<br />
<br />
[[da:Madopskrift]]<br />
[[de:Kochrezept]]<br />
[[fr:Recette]]<br />
[[ja:&#12524;&#12471;&#12500;]]<br />
[[he:&#1502;&#1514;&#1499;&#1493;&#1503;]]</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Experiment&diff=661Experiment2005-08-06T23:58:04Z<p>Laurie Snell: </p>
<hr />
<div>:This is an experiment to see if we can put all of Chance-News (July August) on a single page to make it easier to print it out and to make a pdf version.<br />
<br />
A '''Chance News item''' is a discription of an article in the media that uses probability or statistical concepts. <br />
<br />
A Chance News ite normally consist of:<br />
*The source<br />
*A discussion of the article<br />
*Discussion questions.<br />
<br />
New Çhance News items and improvements to previous items are welcome for the Chance Wiki.<br />
<br />
<br />
<br />
== A sample Chance News ==<br />
:''Title'': <br />
::Fried eggs (two sides done)<br />
::About 5 minutes to prepare.<br />
::Popular breakfast dish in the USA and Western Europe.<br />
::Often served with toast or other fried dishes.<br />
:''Ingredients'':<br />
::2 teaspoons of butter (or olive oil)<br />
::2 or 3 large eggs, depending on appetite<br />
::Seasoning to taste<br />
:''Equipment'':<br />
::A small (10") [[frying pan]]<br />
::A spatula<br />
::Gas ring, at medium heat<br />
:''Method'': <br />
::#Melt the butter in the pan over medium heat<br />
::#Crack open the eggs into the pan and let fry until the yolks begin to harden at the edges (indicated by a lightening in the yolk color).<br />
::#Using the spatula, flip the eggs over and allow to cook for one minute.<br />
::#Add seasoning to taste, and serve.<br />
:''Serves'': <br />
::One<br />
<br />
:''Notes and Variations'':<br />
::It is a cardinal sin for fried eggs to allow the yolk to break. If the cook ensures that the eggs are fresh the yolks will be more 'pert', and less liable to break.<br />
<br />
::For 'Sunnyside Up', do not flip the eggs. Use a mildly lower heat, and cover the pan with a lid for some of the cooking period. An ideal sunnyside up has a runny yolk, but the white should be cooked. Uncooked white (often called jelly) is normally unwanted and less-preferred than a partially cooked yolk, so err on the side of overcooking rather than undercooking the eggs. <br />
<br />
::For a richer taste, try sprinkling with grated parmesan or freshly chopped basil and chives.<br />
<br />
== Other considerations ==<br />
Some notable features of the sample recipe include:<br />
*Ingredients listed in order.<br />
*Pan size specified.<br />
*Cooking temperature specified.<br />
*Criteria for cooking time (until yolks set)<br />
<br />
Stoves/cookers are not normally mentioned in the equipment list.<br />
Indeed, often equipment lists are omitted altogether.<br />
<br />
== What else might be included ==<br />
*Special handling requirements (how are eggs or butter stored? At what temperature should they be when cooking starts?)<br />
*Garnishing or serving advice (add a sprig of parsley for color).<br />
<br />
== Additional facts often included in recipes ==<br />
Recipe writers often add additional facts about the recipe, and, depending upon who you are, they are considered redundant or essential.<br />
<br />
Such facts may include the history of the dish, nutritional information, dietary information, philosophical ramblings about the soul-enriching or health-benefiting properties of the dish, or what wonderful hostess in what particular town first served the dish to the author.<br />
<br />
Nutritional information normally includes [[food energy]], vitamin content, fat content, etc.<br />
<br />
== Where are recipes to be found ==<br />
People have written recipes as recipe cards, recipe books, recipes worked into needlepoint, and computer recipe databases, among others. <br />
Take notes when making your favorite dish and share your recipe in the [[list of recipes]] or Wikibooks [[Wikibooks:Cookbook|cookbook]]. <br />
<br />
The composer [[Leonard Bernstein]] set four recipes to [[music]] in his set of [[song]]s, ''La Bonne Cuisine'' (1947).<br />
<br />
== External links ==<br />
{{Cookbookpar|Recipes}}<br />
<br />
* [http://www.123cuisinez.com 123cuisinez.com - Best recipes of kitchen]<br />
*[http://www.cookbookwiki.com CookbookWiki.com] A community built Recipe Wiki. Over 20,000 recipes.<br />
*[http://www.homebasics.ca/Recipes.asp/ Homebasics Recipes] A Canadian source of fresh and delicious food ideas. 1000's of free recipes.<br />
*[http://www.allrecipes.com/ All Recipes] Over 30,000 editor-approved recipes, advanced searching abilities and rating system.<br />
*[http://www.foodgeeks.com/ ''Foodgeeks.com''] A recipe website with over 7,000 recipes.<br />
*[http://www.stratsplace.com/rogov/art_writing_recipes.html ''The Art of Writing Workable Recipes''] is a history of recipe writing, an analysis of contemporary recipe styles, and a treatise on what constitutes a well-written recipe.<br />
*[http://www.elook.org/recipes/ eLook Recipes] Over 48,000 recipes.<br />
*[http://mythunderbay.ezthemes.com/recipes/index.php Free Recipe Archive]1000's of free access Recipes<br />
*[http://www.anthus.com/Recipes/CompCook.html ''Computerized Cooking''], an analysis of recipe styles, including 14 familiar styles and some unfamiliar computer software styles. Mundie, the author, is a recipe purist who discusses what does and does not belong in a recipe.<br />
*[http://home.snafu.de/gadfly/Veggie.htm ''Veggie Life Magazine''] has published their guidelines for writing recipes. Almost all professional cooking publications have similar guidelines.<br />
*[http://sourceforge.net/projects/anymeal/ ''AnyMeal recipe database software''] is a open-source Linux-software for maintaining more than 100.000 recipes.<br />
*[http://www.visualrecipes.com ''Visual Recipes'']A community of cooks who share their recipes by taking photos of each step of the cooking process. <br />
*[http://www.foodnetwork.com/food/recipes ''Food Network Recipes'']<br />
*[http://www.bbc.co.uk/food/recipes/ ''BBC Food Recipes'']<br />
*[http://www.azpaths.com/features/diamondback-diner ''Diamondback Diner - Southwestern Recipes'']*[http://www.recipesbycathy.com ''Recipes by Cathy''] specializes in healthy but delicious cooking.<br />
*[http://www.cellartastings.com/en/food-spanish-recipes.html Spanish Recipes]<br />
*[http://www.realcajunrecipes.com/ RealCajunRecipes.com features more than 800 recipes from Cajun Country. Photos included.]<br />
*[http://www.activeangler.com/ resources/cooking offers more than 150 delicious fresh fish and seafood recipes.]<br />
*[http://welovefreebies.com/folders/Free_Recipes_and_CookBooks/ Free Recipes and Cookbooks] Directory of free recipes and cookbooks<br />
*[http://www.reciperewards.com/free 1,000's of Quick & Easy Recipes. ] The majority of the recipes have a picture. <br />
*[http://www.turkishcookbook.com Binnur's Turkish Cookbook] Delicious, healthy and easy-to-make Turkish recipes.<br />
<br />
[[Category:Cooking]]<br />
<br />
[[da:Madopskrift]]<br />
[[de:Kochrezept]]<br />
[[fr:Recette]]<br />
[[ja:&#12524;&#12471;&#12500;]]<br />
[[he:&#1502;&#1514;&#1499;&#1493;&#1503;]]</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Experiment&diff=660Experiment2005-08-06T23:42:38Z<p>Laurie Snell: </p>
<hr />
<div>:''This article discusses '''culinary recipes'''. For a discussion of the semiconductor IC '''recipes''' used by the semiconductor fabs, see, for example, [[integrated circuit]].''<br />
<br />
A '''recipe''' is a set of instructions that show how to prepare or make something, especially a culinary dish.<br />
<br />
Modern culinary recipes normally consist of several components:<br />
*The name (and often the locale or [[provenance]]) of the dish,<br />
*How much time it will take to prepare the dish<br />
*The required ingredients along with their quantity<br />
*Equipment and environment needed to prepare the dish<br />
*An ordered list of detailed preparation procedures (called Method).<br />
*The number of servings that the dish will give.<br />
*A rough estimate of the number of [[calorie]]s or [[joule]]s contained per serving.<br />
*A note on how long the dish will keep and its suitability for freezing.<br />
<br />
In the early history of recipes, many of these components were omitted or reduced to a note that required oral instruction, some of which may only have the name and the ingredients of a dish.<br />
<br />
Recipe writers sometimes also list variations of the traditional dish.<br />
<br />
Recipe suggestions are welcome for the Wikibooks [[Wikibooks:Cookbook|Cookbook]].<br />
<br />
== A sample recipe ==<br />
:''Title'': <br />
::Fried eggs (two sides done)<br />
::About 5 minutes to prepare.<br />
::Popular breakfast dish in the USA and Western Europe.<br />
::Often served with toast or other fried dishes.<br />
:''Ingredients'':<br />
::2 teaspoons of butter (or olive oil)<br />
::2 or 3 large eggs, depending on appetite<br />
::Seasoning to taste<br />
:''Equipment'':<br />
::A small (10") [[frying pan]]<br />
::A spatula<br />
::Gas ring, at medium heat<br />
:''Method'': <br />
::#Melt the butter in the pan over medium heat<br />
::#Crack open the eggs into the pan and let fry until the yolks begin to harden at the edges (indicated by a lightening in the yolk color).<br />
::#Using the spatula, flip the eggs over and allow to cook for one minute.<br />
::#Add seasoning to taste, and serve.<br />
:''Serves'': <br />
::One<br />
<br />
:''Notes and Variations'':<br />
::It is a cardinal sin for fried eggs to allow the yolk to break. If the cook ensures that the eggs are fresh the yolks will be more 'pert', and less liable to break.<br />
<br />
::For 'Sunnyside Up', do not flip the eggs. Use a mildly lower heat, and cover the pan with a lid for some of the cooking period. An ideal sunnyside up has a runny yolk, but the white should be cooked. Uncooked white (often called jelly) is normally unwanted and less-preferred than a partially cooked yolk, so err on the side of overcooking rather than undercooking the eggs. <br />
<br />
::For a richer taste, try sprinkling with grated parmesan or freshly chopped basil and chives.<br />
<br />
== Other considerations ==<br />
Some notable features of the sample recipe include:<br />
*Ingredients listed in order.<br />
*Pan size specified.<br />
*Cooking temperature specified.<br />
*Criteria for cooking time (until yolks set)<br />
<br />
Stoves/cookers are not normally mentioned in the equipment list.<br />
Indeed, often equipment lists are omitted altogether.<br />
<br />
== What else might be included ==<br />
*Special handling requirements (how are eggs or butter stored? At what temperature should they be when cooking starts?)<br />
*Garnishing or serving advice (add a sprig of parsley for color).<br />
<br />
== Additional facts often included in recipes ==<br />
Recipe writers often add additional facts about the recipe, and, depending upon who you are, they are considered redundant or essential.<br />
<br />
Such facts may include the history of the dish, nutritional information, dietary information, philosophical ramblings about the soul-enriching or health-benefiting properties of the dish, or what wonderful hostess in what particular town first served the dish to the author.<br />
<br />
Nutritional information normally includes [[food energy]], vitamin content, fat content, etc.<br />
<br />
== Where are recipes to be found ==<br />
People have written recipes as recipe cards, recipe books, recipes worked into needlepoint, and computer recipe databases, among others. <br />
Take notes when making your favorite dish and share your recipe in the [[list of recipes]] or Wikibooks [[Wikibooks:Cookbook|cookbook]]. <br />
<br />
The composer [[Leonard Bernstein]] set four recipes to [[music]] in his set of [[song]]s, ''La Bonne Cuisine'' (1947).<br />
<br />
== External links ==<br />
{{Cookbookpar|Recipes}}<br />
<br />
* [http://www.123cuisinez.com 123cuisinez.com - Best recipes of kitchen]<br />
*[http://www.cookbookwiki.com CookbookWiki.com] A community built Recipe Wiki. Over 20,000 recipes.<br />
*[http://www.homebasics.ca/Recipes.asp/ Homebasics Recipes] A Canadian source of fresh and delicious food ideas. 1000's of free recipes.<br />
*[http://www.allrecipes.com/ All Recipes] Over 30,000 editor-approved recipes, advanced searching abilities and rating system.<br />
*[http://www.foodgeeks.com/ ''Foodgeeks.com''] A recipe website with over 7,000 recipes.<br />
*[http://www.stratsplace.com/rogov/art_writing_recipes.html ''The Art of Writing Workable Recipes''] is a history of recipe writing, an analysis of contemporary recipe styles, and a treatise on what constitutes a well-written recipe.<br />
*[http://www.elook.org/recipes/ eLook Recipes] Over 48,000 recipes.<br />
*[http://mythunderbay.ezthemes.com/recipes/index.php Free Recipe Archive]1000's of free access Recipes<br />
*[http://www.anthus.com/Recipes/CompCook.html ''Computerized Cooking''], an analysis of recipe styles, including 14 familiar styles and some unfamiliar computer software styles. Mundie, the author, is a recipe purist who discusses what does and does not belong in a recipe.<br />
*[http://home.snafu.de/gadfly/Veggie.htm ''Veggie Life Magazine''] has published their guidelines for writing recipes. Almost all professional cooking publications have similar guidelines.<br />
*[http://sourceforge.net/projects/anymeal/ ''AnyMeal recipe database software''] is a open-source Linux-software for maintaining more than 100.000 recipes.<br />
*[http://www.visualrecipes.com ''Visual Recipes'']A community of cooks who share their recipes by taking photos of each step of the cooking process. <br />
*[http://www.foodnetwork.com/food/recipes ''Food Network Recipes'']<br />
*[http://www.bbc.co.uk/food/recipes/ ''BBC Food Recipes'']<br />
*[http://www.azpaths.com/features/diamondback-diner ''Diamondback Diner - Southwestern Recipes'']*[http://www.recipesbycathy.com ''Recipes by Cathy''] specializes in healthy but delicious cooking.<br />
*[http://www.cellartastings.com/en/food-spanish-recipes.html Spanish Recipes]<br />
*[http://www.realcajunrecipes.com/ RealCajunRecipes.com features more than 800 recipes from Cajun Country. Photos included.]<br />
*[http://www.activeangler.com/ resources/cooking offers more than 150 delicious fresh fish and seafood recipes.]<br />
*[http://welovefreebies.com/folders/Free_Recipes_and_CookBooks/ Free Recipes and Cookbooks] Directory of free recipes and cookbooks<br />
*[http://www.reciperewards.com/free 1,000's of Quick & Easy Recipes. ] The majority of the recipes have a picture. <br />
*[http://www.turkishcookbook.com Binnur's Turkish Cookbook] Delicious, healthy and easy-to-make Turkish recipes.<br />
<br />
[[Category:Cooking]]<br />
<br />
[[da:Madopskrift]]<br />
[[de:Kochrezept]]<br />
[[fr:Recette]]<br />
[[ja:&#12524;&#12471;&#12500;]]<br />
[[he:&#1502;&#1514;&#1499;&#1493;&#1503;]]</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=I_was_quoting_the_statistics,_I_wasn%27t_pretending_to_be_a_statistician&diff=549I was quoting the statistics, I wasn't pretending to be a statistician2005-07-31T12:32:14Z<p>Laurie Snell: </p>
<hr />
<div>[http://news.bbc.co.uk/2/hi/health/4679113.stm Sir Roy Meadow struck off by GMC]<br><br />
BBC News, 15 July 2005<br />
<br />
[http://pass.maths.org.uk/issue21/features/clark/ Beyond reasonable doubt]<br><br />
Plus Magazine, 2002<br><br />
Helen Joyce<br />
<br />
[http://www.sciencemag.org/cgi/content/summary/309/5734/543a Flawed Statistics in Murder Trial May Cost Expert His Medical License]<br><br />
Science, 22 July 2005<br><br />
<br />
Multiple sudden infant deaths--coincidence or beyond coincidence<br><br />
Paediatric and Perinatal Epidemiology 2004, 18, 320-326<br><br />
Roy Hill<br />
<br />
___________________________________________________________________________________<br />
<br />
Sir Roy Meadow is a pediatrician, well known for his research in child abuse. The BBC article reports that the UK General Medical Council (GMC) has found Sir Roy guilty of serious professional misconduct and has "struck him off" the medical registry. If upheld under appeal, this will prevent Meadow from practicing medicine in the UK.<br />
<br />
This decision was based on a flawed statistical estimate that Meadow made while testifying as an expert witness in a 1999 trial in which a Sally Clark was found guilty of murdering her two baby boys and given a life sentence. <br />
<br />
To understand Meadow's testimony we need to know what a SIDS (sudden infant death syndrome) is. The name SIDS was proposed by the pathologist Bruce Beckwih at a conference in 1969 and the definition, which is still current, along with many others,was formulated at the conference by Beckwith and others as follows: <br />
<br />
<blockquote>The sudden death of a baby that is unexpected by history and in whom a<br> thorough post-mortem examination fails to demonstrate an adequate cause of death. </blockquote><br />
<br />
The death of Sally Clark's first baby was reported as a cot death, which is another name for SIDS. Then when her second baby died she was arrested and tried for murdering both her children.<br />
<br />
We were not able to find a transcript for the original trial but from Lexis Nexis we found transcripts of two appeals that the Clarks made, one in October 2000 that they lost, and the other in April 2003 which they won releasing Sally after four anda half years in jail. The 2003 transcript reported on the statistical testimony in the original trial as follows:<br />
<br />
<blockquote> Professor Meadow was asked about some statistical information as to the happening of two cot deaths within the <br />
same family, which at that time was about to be published in a report of a government funded multi--disciplinary research <br />
team, the Confidential Enquiry into Sudden Death in Infancy (CESDI) entitled 'Sudden Unexpected Deaths in Infancy' to <br />
which the professor was then writing a Preface. Professor Meadow said that it was 'the most reliable study and easily the <br />
largest and in that sense the latest and the best' ever done in this country. <br><br><br />
<br />
It was explained to the jury that there were factors that were suggested as relevant to the chances of a SIDS death within a given family; namely the age of the mother, whether there was a smoker in the household and the absence of a wage-earner in the family.<br><br><br />
<br />
None of these factors had relevance to the Clark family and Professor Meadow was asked if a <br />
figure of 1 in 8,543 reflected the risk of there being a single SIDS within such a family. He agreed that it was. A table <br />
from the CESDI report was placed before the jury. He was then asked if the report calculated the risk of two infants dying <br />
of SIDS in that family by chance. His reply was: 'Yes, you have to multiply 1 in 8,543 times 1 in 8,543 and I think it <br />
gives that in the penultimate paragraph. It points out that it's approximately a chance of 1 in 73 million.' <br><br><br />
<br />
It seems that at this point Professor Meadow's voice was dropping and so the figure was repeated and then <br />
Professor Meadow added: 'In England, Wales and Scotland there are about say 700,000 live births a year, so it is saying <br />
by chance that happening will occur about once every hundred years.' <br><br><br />
<br />
Mr. Spencer [for the prosecution] then pointed to the suspicious features alleged by the Crown in this present case and asked: 'So is <br />
this right, not only would the chance be 1 in 73 million but in addition in these two deaths there are features, which wuld <br />
be regarded as suspicious in any event?' He elicited the reply 'I believe so'. <br><br><br />
<br />
All of this evidence was given without objection from the defence but Mr. Bevan (who represented the <br />
Appellant at trial and at the first appeal but not at ours) cross--examined the doctor. He put to him figures from other <br />
research that suggested that the figure of 1 in 8,543 for a single cot death might be much too high. He then dealt with the <br />
chance of two cot deaths and Professor Meadow responded: <br />
'This is why you take what's happened to all the children into account, and that is why you end up saying the chance <br />
of the children dying naturally in these circumstances is very, very long odds indeed one in 73 million.' <br />
He then added: <br><br><br />
<br />
'. . . it's the chance of backing that long odds outsider at the Grand National, yu know; let's say it's a 80 to 1 chance, <br />
you back the winner last year, then the next year there's another horse at 80 to 1 and it is still 80 to 1 and you back it again <br />
and it wins. Now here we're in a situation that, you know, to get to these odds of 73 million you've got to back that 1 in 80 <br />
chance four years running, so yes, you might be very, very lucky because each time it's just been a 1 in 80 chance and you <br />
know, you've happened to have won it, but the chance of it happening four years running we all know is extraordinarily <br />
unlikely. So it's the same with these deaths. You have to say two unlikely events have happened and together it's very, <br />
very, very unlikely.' <br><br><br />
<br />
The trial judge clearly tried to divert the jury away from reliance on this statistical evidence. He said: <br />
'I should, I think, members of the jury just sound a word of caution about the statistics. However compelling you may <br />
find them to be, we do not convict people in these courts on statistics. It would be a terrible day if that were so. If there is <br />
one SIDS death in a family, it does not mean that there cannot be another one in the same family.' </blockquote><br />
<br />
Note that Meadow obtained the odds of 73 million to one from the CESDI report so there is some truth to the statement "I was quoting the statistics, I wasn't pretending to be a statistician” that Meadow made to the General Medical Council. Note also that both Meadow and the Judge took this statistic seriously and must have felt that it was evidence that Sally Clark was guilty. This was also true of the press. The Sunday Mail (Queenstand, Australia) had an article titled "Mum killed her babies" in which we read: <br />
<br />
<BLOCKQUOTE>Medical experts gave damning evidence that the odds of both children dying from cot death were 73 million to one.</blockquote><br />
<br />
There are two obvious problems with this 1 in 73 million statistic: (1) Because of environmental and genetics effects it seems very unlikely that the a SIDS death for a families the first baby and for their second baby are independent and (2) These odds might suggest to the jury that there is a 1 in 74 million chance that Sally Clark is innocent. This is, the well-known prosecuter's paradox. In addition, the medical experts testimonies were very technical and some were contradictory. The 1 in 73 million odds were something the jury would at least feel that they could understand. <br />
<br />
Of course these odds of 73 million to 1 for SIDS teaths are useless to the jury in assessing guilt unless they are also given the corresponding odds that the deaths were the result of murders. In his article on the Sally Clark trial. Professor Roy Hill estimated that, for a randomly chosen family with two baby deaths, the probability that the deaths are the result of SIDS is about 10 times more likely than the probability that they are the result of murders. Thus, if this kind of statistical evidence means anything, it suggests that Sally Clark is innocent. <br />
<br />
The Clarks had their first appeal in 2 October 2000. By this time they realized that they had to have there own statisticians as expert witnesses. They chose Ian Evett from the Forensic Science Service and Phillip Dawid, Professor of Statistics at the Department of Statistical Science, University College London. Both of these statisticians have specialized in statistical evidence in the courts. In his report Dawid gave a very clear description of what would be required to obtain a reasonable estimate of the probability of two SIDS deaths in a randomly chosen family with two babies. He emphasized that it would be important also to have some estimate of the variability of this estimate. Then he gave an equally clear discussion on the relevance of this probability, emphasizing the need for the corresponding probability of two murders in a family with two children. His conclusion was:<br />
<br />
<blockquote>The figure “1 in 73 million” quoted in Sir Roy Meadow's testimony at trial, as the probability of two babies both dying of SIDS in a family like Sally Clark's, was highly misleading and prejudicial. The value of this probability has not been estimated with anything like the precision suggested, and could well be very much higher. But, more important, the figure was presented with no explanation of the logically correct use of such information - which is very different from what a simple intuitive reaction might suggest. In particular, such a figure could only be useful if compared with a similar figure calculated under the alternative hypothesis that both babies were murdered. Even though assessment of the relevant probabilities may be difficult, there is a clear and well-established statistical logic for combining them and making appropriate inferences from them, which was not appreciated by the court. </blockquote><br />
<br />
These two statisticians were not allowed to appear in the court proceedings but only to have their reports read. <br />
<br />
The Clarks Ground 3a for the appeal dealt with the statistical issues including Meadow's incorrect calculation and the Judge failing to warn the jury against the "prosecutor's fallacy".<br />
<br />
Concerning the miscalulation of the odds for two SIDS in a family of two children he remarks that this was already known and all that really mattered was that appearance of two SIDS deaths is unusual.<br />
<br />
He dismisses the prosecutors fallacy with the remark:<br />
<br />
He [Everett] makes the obvious point that the evidential material in Table 3.58 tell us nothing whatsoever as to the guilt or innocence of the appellant. <br />
<br />
He concludes:<br />
<br />
<blockquote> Thus we do not think that the matters raised under Ground 3(a) are capable of affecting the safety of the <br />
convictions. They do not undermine what was put before the jury or cast a fundamentally different light on it. Even if <br />
they had been raised at trial, the most that could be expected to have resulted would be a direction to the jury that the issue <br />
was the broad one of rarity, to which the precise degree of probability was unnecessary. </blockquote><br />
<br />
<br />
<br />
<br />
<br />
References<br />
<br />
Transcript for the 2000 and 2003 appeals can be obtained from Lexis Nexis following the following route:<br />
<br />
Open Lexis Nexis<br />
<br />
Choose "Legal Research" from the sidebar<br />
<br />
From "Case Law" choose "Get a Case"<br />
<br />
Choose" Commonwealth and Foreign Nations" from the sidebar<br />
<br />
Choose "Sally Clark” for the " Keyword"<br />
<br />
Choose "UK Cases" for the "Source"<br />
<br />
Choose "Previous five years” for the "Date."<br />
<br />
The two " r v Clarks" are the appeals.<br />
<br />
To be continued<br />
<br />
Retrieved from "http://chance.dartmouth.edu/chancewiki/index.php/I_was_quoting_the_statistics%2C_I_wasn%27t_pretending_to_be_a_statisitcian"<br />
The two " r v Clarks" are the appeals. <br />
To be continued<br />
<br />
Retrieved from "http://chance.dartmouth.edu/chancewiki/index.php/I_was_quoting_the_statistics%2C_I_wasn%27t_pretending_to_be_a_statisitcian"</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=I_was_quoting_the_statistics,_I_wasn%27t_pretending_to_be_a_statistician&diff=548I was quoting the statistics, I wasn't pretending to be a statistician2005-07-31T12:14:55Z<p>Laurie Snell: </p>
<hr />
<div>[http://news.bbc.co.uk/2/hi/health/4679113.stm Sir Roy Meadow struck off by GMC]<br><br />
BBC News, 15 July 2005<br />
<br />
[http://pass.maths.org.uk/issue21/features/clark/ Beyond reasonable doubt]<br><br />
Plus Magazine, 2002<br><br />
Helen Joyce<br />
<br />
[http://www.sciencemag.org/cgi/content/summary/309/5734/543a Flawed Statistics in Murder Trial May Cost Expert His Medical License]<br><br />
Science, 22 July 2005<br><br />
<br />
Multiple sudden infant deaths--coincidence or beyond coincidence<br><br />
Paediatric and Perinatal Epidemiology 2004, 18, 320-326<br><br />
Roy Hill<br />
<br />
___________________________________________________________________________________<br />
<br />
Sir Roy Meadow is a pediatrician, well known for his research in child abuse. The BBC article reports that the UK General Medical Council (GMC) has found Sir Roy guilty of serious professional misconduct and has "struck him off" the medical registry. If upheld under appeal, this will prevent Meadow from practicing medicine in the UK.<br />
<br />
This decision was based on flawed statistical estimate that Meadow made while testifying as an expert witness in a 1999 trial in which a Sally Clark was found guilty of murdering her two baby boys and given a life sentence. <br />
<br />
To understand his testimony we need to know what a SIDS (sudden infant death syndrome) is. The name SIDS was proposed by the pathologist Bruce Beckwih at a conference in 1969 and the definition, which is still current, along with many others,was formulated at the conference by Beckwith and others as follows: <br />
<br />
<blockquote>The sudden death of a baby that is unexpected by history and in whom a<br> thorough post-mortem examination fails to demonstrate an adequate cause of death. </blockquote><br />
<br />
The death of Sally Clark's first baby was reported as a cot death, which is another name for SIDS. Then when her second baby died she was arrested and tried for murdering both her children.<br />
<br />
We were not able to find a transcript for the original trial but from Lexis Nexis we found transcripts of two appeals that the Clarks made, one in October 2000 that they lost, and the other in April 2003 which they won and Sally Clark was released from jail. The 2003 transcript reported on the statistical testimony in the original trial as follows:<br />
<br />
<blockquote> Professor Meadow was asked about some statistical information as to the happening of two cot deaths within the <br />
same family, which at that time was about to be published in a report of a government funded multi--disciplinary research <br />
team, the Confidential Enquiry into Sudden Death in Infancy (CESDI) entitled 'Sudden Unexpected Deaths in Infancy' to <br />
which the professor was then writing a Preface. Professor Meadow said that it was 'the most reliable study and easily the <br />
largest and in that sense the latest and the best' ever done in this country. <br><br><br />
<br />
It was explained to the jury that there were factors that were suggested as relevant to the chances of a SIDS death within a given family; namely the age of the mother, whether there was a smoker in the household and the absence of a wage-earner in the family.<br><br><br />
<br />
None of these factors had relevance to the Clark family and Professor Meadow was asked if a <br />
figure of 1 in 8,543 reflected the risk of there being a single SIDS within such a family. He agreed that it was. A table <br />
from the CESDI report was placed before the jury. He was then asked if the report calculated the risk of two infants dying <br />
of SIDS in that family by chance. His reply was: 'Yes, you have to multiply 1 in 8,543 times 1 in 8,543 and I think it <br />
gives that in the penultimate paragraph. It points out that it's approximately a chance of 1 in 73 million.' <br><br><br />
<br />
It seems that at this point Professor Meadow's voice was dropping and so the figure was repeated and then <br />
Professor Meadow added: 'In England, Wales and Scotland there are about say 700,000 live births a year, so it is saying <br />
by chance that happening will occur about once every hundred years.' <br><br><br />
<br />
Mr. Spencer [for the prosecution] then pointed to the suspicious features alleged by the Crown in this present case and asked: 'So is <br />
this right, not only would the chance be 1 in 73 million but in addition in these two deaths there are features, which wuld <br />
be regarded as suspicious in any event?' He elicited the reply 'I believe so'. <br><br><br />
<br />
All of this evidence was given without objection from the defence but Mr. Bevan (who represented the <br />
Appellant at trial and at the first appeal but not before us) cross--examined the doctor. He put to him figures from other <br />
research that suggested that the figure of 1 in 8,543 for a single cot death might be much too high. He then dealt with the <br />
chance of two cot deaths and Professor Meadow responded: <br />
'This is why you take what's happened to all the children into account, and that is why you end up saying the chance <br />
of the children dying naturally in these circumstances is very, very long odds indeed one in 73 million.' <br />
He then added: <br><br><br />
<br />
'. . . it's the chance of backing that long odds outsider at the Grand National, yu know; let's say it's a 80 to 1 chance, <br />
you back the winner last year, then the next year there's another horse at 80 to 1 and it is still 80 to 1 and you back it again <br />
and it wins. Now here we're in a situation that, you know, to get to these odds of 73 million you've got to back that 1 in 80 <br />
chance four years running, so yes, you might be very, very lucky because each time it's just been a 1 in 80 chance and you <br />
know, you've happened to have won it, but the chance of it happening four years running we all know is extraordinarily <br />
unlikely. So it's the same with these deaths. You have to say two unlikely events have happened and together it's very, <br />
very, very unlikely.' <br><br><br />
<br />
The trial judge clearly tried to divert the jury away from reliance on this statistical evidence. He said: <br />
'I should, I think, members of the jury just sound a word of caution about the statistics. However compelling you may <br />
find them to be, we do not convict people in these courts on statistics. It would be a terrible day if that were so. If there is <br />
one SIDS death in a family, it does not mean that there cannot be another one in the same family.' </blockquote><br />
<br />
Note that Meadow obtained the odds of 73 million to one from the CESDI report so there is some truth to the statement "I was quoting the statistics, I wasn't pretending to be a statistician” that Meadow made to the General Medical Council. Note also that both Meadow and the Judge took this statistic seriously and must have felt that it was evidence that Sally Clark was guilty. This was also true of the press. The Sunday Mail (Queenstand, Australia) had an article titled "Mum killed her babies" in which we read: <br />
<br />
<BLOCKQUOTE>Medical experts gave damning evidence that the odds of both children dying from cot death were 73 million to one.</blockquote><br />
<br />
There are two obvious problems with this 1 in 73 million statistic: (1) Because of environmental and genetics effects it seems very unlikely that the a SIDS death for a families the first baby and for their second baby are independent and (2) These odds might suggest to the jury that there is a 1 in 74 million chance that Sally Clark is innocent. This is, of course, the well-known prosecuter's paradox. In addition, the medical experts testimonies were very technical and some were contradictory. The 1 in 73 million odds were something the jury would at least understand. <br />
<br />
Of course these odds of 73 million to 1 for SIDS teaths are useless to the jury in assessing guilt unless they are also given the corresponding odds that the deaths were the result of murders. In an article on the Sally Clark trial. Professor Roy Hill estimated that, for a randomly chosen family with two baby deaths, the probability that the deaths are the result of SIDS is about 10 times more likely than that probability that they are the result of murders. Thus, if this kind of statistical evidence means anything, it suggests that Sally Clark is innocent. <br />
<br />
The Clarks had their first appeal in 2 October 2000. By this time the Clarks realized that they had to have there own statisticians as expert witnesses. They chose Ian Everett from the Forensic Science Service and Phillip Dawid, Professor of Statistics at the Department of Statistical Science, University College London. Both of these statisticians have specialized in statistical evidence in the courts. In his report Dawid gave a very clear description of what would be required to obtain a reasonable estimate of the probability of two SIDS deaths in a randomly chosen family with two babies. He emphasized that it would be important also to have some estimate of the variability of this estimate. Then he gave an equally clear discussion on the relevance of this probability, emphasizing the need for the corresponding probability of two murders in a family with two children. His conclusion was:<br />
<br />
<blockquote>The figure “1 in 73 million” quoted in Sir Roy Meadow's testimony at trial, as the probability of two babies both dying of SIDS in a family like Sally Clark's, was highly misleading and prejudicial. The value of this probability has not been estimated with anything like the precision suggested, and could well be very much higher. But, more important, the figure was presented with no explanation of the logically correct use of such information - which is very different from what a simple intuitive reaction might suggest. In particular, such a figure could only be useful if compared with a similar figure calculated under the alternative hypothesis that both babies were murdered. Even though assessment of the relevant probabilities may be difficult, there is a clear and well-established statistical logic for combining them and making appropriate inferences from them, which was not appreciated by the court. </blockquote><br />
<br />
These two statisticians were not allowed to appear in the court proceedings but only to have their reports read. <br />
<br />
The Clarks Ground 3a for the appeal dealt with the statistical issues including Meadow's incorrect calculation and the Judge failing to warn the jury against the "prosecutor's fallacy".<br />
<br />
Concerning the miscalulation of the odds for two SIDS in a family of two children he remarks that this was already known and all that really mattered was that appearance of two SIDS deaths is unusual.<br />
<br />
He dismisses the prosecutors fallacy with the remark:<br />
<br />
He [Everett] makes the obvious point that the evidential material in Table 3.58 tell us nothing whatsoever as to the guilt or innocence of the appellant. <br />
<br />
He concludes:<br />
<br />
<blockquote> Thus we do not think that the matters raised under Ground 3(a) are capable of affecting the safety of the <br />
convictions. They do not undermine what was put before the jury or cast a fundamentally different light on it. Even if <br />
they had been raised at trial, the most that could be expected to have resulted would be a direction to the jury that the issue <br />
was the broad one of rarity, to which the precise degree of probability was unnecessary. </blockquote><br />
<br />
<br />
<br />
<br />
<br />
References<br />
<br />
Transcript for the 2000 and 2003 appeals can be obtained from Lexis Nexis following the following route:<br />
<br />
Open Lexis Nexis<br />
<br />
Choose "Legal Research" from the sidebar<br />
<br />
From "Case Law" choose "Get a Case"<br />
<br />
Choose" Commonwealth and Foreign Nations" from the sidebar<br />
<br />
Choose "Sally Clark” for the " Keyword"<br />
<br />
Choose "UK Cases" for the "Source"<br />
<br />
Choose "Previous five years” for the "Date."<br />
<br />
The two " r v Clarks" are the appeals.<br />
<br />
To be continued<br />
<br />
Retrieved from "http://chance.dartmouth.edu/chancewiki/index.php/I_was_quoting_the_statistics%2C_I_wasn%27t_pretending_to_be_a_statisitcian"<br />
The two " r v Clarks" are the appeals. <br />
To be continued<br />
<br />
Retrieved from "http://chance.dartmouth.edu/chancewiki/index.php/I_was_quoting_the_statistics%2C_I_wasn%27t_pretending_to_be_a_statisitcian"</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Chance_News_(July-August_2005)&diff=588Chance News (July-August 2005)2005-07-31T12:10:24Z<p>Laurie Snell: </p>
<hr />
<div>Under construction. See [[Chance News (May-June 2005)]] for additional recent chance news.<br />
<br />
<blockquote> Numbers are like people; torture them enough and they'll tell you anything.</blockquote><br />
<br />
*[[Forsooth (July-August 2005)]]<br />
*[[A probability problem]]<br />
*[[ Misperception of minorities and immigrants]]<br />
*[[ I was quoting the statistics, I wasn't pretending to be a statistician]]<br />
*[[ What women want]]<br />
*[[Rules of engagement - modelling conflict]]<br />
*[[How people respond to terrorist attacks]]</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Marilyn_answers_a_lottery_question&diff=13119Marilyn answers a lottery question2005-07-30T17:59:54Z<p>Laurie Snell: </p>
<hr />
<div>Ask Marilyn<br><br />
[http://archive.parade.com/2005/0410/0410_askmarilyn.html Parade, April 10, 2005]<br><br />
Marilyn vos Savant.<br />
<br />
A reader poses the following question: <br />
<blockquote><br />
My wife and I attended a "reverse raffle," in which everyone bought a number. Numbered balls were then drawn out of a bin one at a time. The last number would be the winner. But when the organizers got down to the last couple of dozen balls, they discovered that some numbered balls had been overlooked. So they added those balls to the bin and continued the drawing. Didn’t the added balls have a much better chance of winning?<br />
</blockquote><br />
<br />
Marilyn responds, "Yes, they did. But because everyone had an equal chance of his or her numbered ball being one of those overlooked, the last-minute addition made no difference to anyone’s chance of winning. The raffle was still fair."<br />
<br />
Marilyn's answers to probability problems often stir up controversy, and this was no exception. The discussion continues in the column below. <br />
<br />
----<br />
Ask Marilyn.<br><br />
[http://archive.parade.com/askmarilyn_archive/2005/0605.html Parade, June 5, 2005]<br><br />
Marilyn vos Savant.<br />
<br />
A reader had this objection to Marilyn's answer:<br />
<blockquote><br />
Marilyn: I disagree with your answer. Participants whose balls were left out had a higher likelihood of winning. Regardless of whether they had a fair chance of being overlooked, the raffle was not mathematically fair. Assume there were 20 participants. The odds of winning should be one in 20 throughout the game for each contestant. Put 15 balls in a jar and withdraw 10. Then add the missing five.<br />
<br />
The first 15 balls had a two-in-three chance of “not winning” until the five balls were added. The missing five balls had a zero chance of “not winning” during that time, then had a one-in-10 chance of winning after they were added. Only the five balls that were in the bowl the entire time had a one-in-20 chance of winning.<br />
</blockquote><br />
<br />
Marilyn says her original answer was correct, and asks the reader to "consider a scenario in which the added balls were withheld (on purpose) instead of overlooked." She says. "Your explanation works in that case. So it cannot work in the case when the added balls were merely overlooked."<br />
<br />
DISCUSSION QUESTIONS:<br />
<br />
(1) Do you understand Marilyn's last response?<br />
<br />
(2) The reader is actually giving conditional probabilities. Do you agree with their values?<br />
<br />
(3) Now consider the reader's set-up, under Marilyn's original assumption that each ball had an equal chance of being overlooked in the first stage. Thus, there are 20 balls, and 15 are initially selected at random and placed in the bin. Now 10 are drawn one at a time at random from the bin. At this point, the 5 balls originally omitted are added to the bin. Then balls are drawn one at a time at random from the bin. Looking at the whole process, does each ball have a one-in-20 chance of being the last ball in the bin?<br />
<br />
(4) Upon realizing the correct answer to Marilyn's problem, a chance news reader suggested that this meant that the famous 1970 Vietnam lottery was fair also. Recall that in this lottery 366 balls with the possible dates in a year were put in a bowl and mixed up. Then the balls were drawn out one at a time and the dates on the balls determined the order in which draftees would be called up. It was estimated that those with birthdays were on the last third of the balls drawn would not be called up at all. Å statistical analysis suggested that the balls were not well mixed and as a result those born in the early months were significently more likely to be called up than those born in the later months. But our reader said that, since our birthdays are random, the lottery was still fair. Do you agree?<br />
<br />
P.S. You can read the ''New York Times'' account of the statistical challenge of this lottery [http://www.dartmouth.edu/~chance/chance_news/recent_news/chance_news_6.10.html#draftlottery here] and a nice article by Norton Starr on how to use this lottery in a statistical class [http://www.amstat.org/publications/jse/v5n2/datasets.starr.html here].</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=ChanceWiki:About&diff=1411ChanceWiki:About2005-06-05T17:47:36Z<p>Laurie Snell: </p>
<hr />
<div>The Chance Wiki provides reviews of articles in the media that use probability or statistical concepts (chance news). It's purpose is to help the general public better understand chance news and also to allow teachers of probability or statistics to use current chance news in their courses.</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Help:Contents&diff=405Help:Contents2005-06-03T14:19:34Z<p>Laurie Snell: </p>
<hr />
<div>You can find help on most topics by going to [http://en.wikipedia.org/wiki/Wikipedia:Tutorial Wiipedia Tutorial.] <br />
<br />
Here are some things that are in the tutorial that we found particularly usefull.<br />
*[http://en.wikibooks.org/wiki/Quick_Edit_Guide Quick Edit Guide]<br />
*[http://en.wikipedia.org/wiki/Wikipedia:External_links#External_links_section External Links] <br />
*[http://en.wikipedia.org/wiki/Wikipedia:Manual_of_Style_%28links%29#Internal_links Internal Links]<br />
*[http://en.wikipedia.org/wiki/Wikipedia:Picture_tutorial How to Use images]<br />
*[http://en.wikipedia.org/wiki/Wikipedia:How_to_use_tables How to use tables]<br />
*[http://en.wikipedia.org/wiki/Wikipedia:TeX_markup Special characters, mathematics]</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Template&diff=353Template2005-05-31T14:14:03Z<p>Laurie Snell: </p>
<hr />
<div>Mix math and medicine and create confusion<br><br />
New York Times, April 26, 2005, F 11<br><br />
Richard Friedman, M.D<br />
<br />
This article provides an interesting exchange between a doctor (Doctor Friedman) and a statistician (Judith Singer).<br />
<br />
(The break marks are necessary because Wiki only make a new line when it sees a blank spaces. Do not leave a space before typing a line. If you do you will get a box around the line!)<br />
<br />
To make a link to a website, for example to the [http://www.dartmouth.edu/~chance Chance Website] Website, start with the URL, add a space, and add name of the website. Put this whole thing in brackets. <br />
<br />
There are two ways to indent a quotation. The first is to indent each line using :, ::, ::: depending on how much you want to indent it.<br />
<br />
::We've heard that a million monkeys at a million keyboards could <br />
::produce the complete works of Shakespeare.Now, thanks to the<br />
::Internet, we know that is not true. ~ Robert Wilensky<br />
<br />
The other is to use the web blockquote.<br />
<blockquote><br />
We've heard that a million monkeys at a million keyboards could produce the complete works of Shakespeare. Now, thanks to the<br />
Internet, we know that is not true. ~ Robert Wilensky<br />
</blockquote><br />
<br />
There are two ways to add images. If you have a URL for the image you can just give this without any brackets. For example:<br />
<br />
<center> http://www.dartmouth.edu/~chance/wikividios/primeWSJ.jpg</center><br />
<br />
The other method is to upload the image. For this you have to login and use the "Upload file" that appears on the sidebar after you register. If you use this method you can adjust the size and make other adjustments explained in the Help available from the sidebar. Here is an example:<br />
[[Image:news.gif |200px]]<br />
<br />
It is nice to add a discussion question or two. The format for this is:<br />
<br />
DISCUSSION:<br />
<br />
(1) Do you think this Template will be helpful?<br />
<br />
(2) What have I left out?</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=How_to_submit_a_new_article_or_edit_an_existing_article&diff=940How to submit a new article or edit an existing article2005-05-31T14:12:29Z<p>Laurie Snell: </p>
<hr />
<div>To modify a page choose "edit" from the top of the page and make the desired changes. Then choose "Show preview" from the bottom of the page. If you are satified with your changes choose "Save" at the bottom of the page. In the Summary box indicate the type of change you made. You can modify the content of the article or add discussion questions that you might think of while reading the artice. For additional help in editing a page, including how to add pictures, links, special characters, etc., choose "Help" from the side box. <br />
<br />
To add a new article, choose a name for the article. This can be the name used by the news media or a name chosen by you. Then from the Main Page choose the most recent Chance News. Using "edit" add the name for your article to the list of the previous items. Note that we do not put a period at the end of the name. Then click on your title and a blank page will turn up. Choose edit from the top of this page and add the source of your article and your comments about it. The page [[Template]] provides examples of formating that you might meet in adding your article. To see the source you need to choose edit for this page. Additional help can be obtained from the Help page available from the sidebar or [[http://chance.dartmouth.edu/chancewiki/index.php/Help:Contents here]] <br />
<br />
The "discussion" at the top of a page allows can be used to add comments related to that page. The discussion page for an article can be used for comments about the article, for the current Chance News page to suggest additional articles, and for the Main page to comment on the Chance Wiki itself.<br />
<br />
Copyright. Since, in most cases, we are doing a critical analysis of an article, fair use should allow us to make reasonable quotes, graphics, images etc. from the article without the permission of the copyright owner. You can read one lawyer's interpretation of fair use as it applies to Chance News [http://www.dartmouth.edu/~chance/Fair_Use/fair.html here]. Of course we should be sure to give the source of anything we use. When you upload an image you will be asked to indicate if you are doing it under fair use or you have permission from the copyright owner and also to give the source. This information will be made known to the reader by clicking on the image. <br />
<br />
Good luck and remember it will be easier next time!</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Template&diff=332Template2005-05-31T13:46:13Z<p>Laurie Snell: </p>
<hr />
<div>Mix math and medicine and create confusion<br><br />
New York Times, April 26, 2005, F 11<br><br />
Richard Friedman, M.D<br />
<br />
This article provides an interesting exchange between a doctor (Doctor Friedman) and a statistician (Judith Singer).<br />
<br />
(The break marks are necessary because Wiki only make a new line when it sees a blank spaces. Do not leave a space before typing a line. If you do you will get a box around the line!)<br />
<br />
To make a link to a website, for example to the [http://www.dartmouth.edu/~chance Chance Website] Website, start with the URL, add a space, and add name of the website. Put this whole thing in brackets. <br />
<br />
There are two ways to indent a quotation. The first is to indent each line using :, ::, ::: depending on how much you want to indent it.<br />
<br />
::We've heard that a million monkeys at a million keyboards could <br />
::produce the complete works of Shakespeare.Now, thanks to the<br />
::Internet, we know that is not true. ~ Robert Wilensky<br />
<br />
The other is to use the web blockqote.<br />
<blockquote><br />
We've heard that a million monkeys at a million keyboards could produce the complete works of Shakespeare. Now, thanks to the<br />
Internet, we know that is not true. ~ Robert Wilensky<br />
</blockquote><br />
<br />
There are two ways to add images. If you have a URL for the image you can just give this without any brackets. For example:<br />
<br />
<center> http://www.dartmouth.edu/~chance/wikividios/primeWSJ.jpg</center><br />
<br />
The other method is to upload the image. For this you have to login and use the "Upload file" that appears on the sidebar after you register. If you use this method you can adjust the size and make other adjustments explained in the Help available from the sidebar. Here is an example:<br />
[[Image:news.gif |200px]]<br />
<br />
It is nice to add a discussion question or two. The format for this is:<br />
<br />
DISCUSSION:<br />
<br />
(1) Do you think this Template will be helpful?<br />
<br />
(2) What have I left out?</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Template&diff=330Template2005-05-31T13:43:52Z<p>Laurie Snell: </p>
<hr />
<div>Mix math and medicine and create confusion<br><br />
New York Times, April 26, 2005, F 11<br><br />
Richard Friedman, M.D<br />
<br />
This article provides an interesting exchange between a doctor (Doctor Friedman) and a statistician (Judith Singer).<br />
<br />
(The break marks are necessary because Wiki only make a new line when it sees a blank spaces. Do not leave a space before typing a line. If you do you will get a box around the line!)<br />
<br />
To make a link to a website, for example to the [http://www.dartmouth.edu/~chance Chance Website] Website, start with the URL, add a space, and add name of the website. Put this whole thing in brackets. <br />
<br />
There are two ways to indent a quotation. The first is to indent each line using :, ::, ::: depending on how much you want to indent it.<br />
<br />
::We've heard that a million monkeys at a million keyboards could <br />
::produce the complete works of Shakespeare.Now, thanks to the<br />
::Internet, we know that is not true. ~ Robert Wilensky<br />
<br />
The other is to use the web blockqote.<br />
<blockquote><br />
We've heard that a million monkeys at a million keyboards could produce the complete works of Shakespeare. Now, thanks to the<br />
Internet, we know that is not true. ~ Robert Wilensky<br />
</blockquote><br />
<br />
There are two ways to add images. If you have a URL for the image you can just give this without any brackets. For example:<br />
<br />
<center> http://www.dartmouth.edu/~chance/wikividios/primeWSJ.jpg</center><br />
<br />
The other method is to upload the image. For this you have to login and use the "Upload file" that appears on the sidebar after you register. If you use this method you can adjust the size and make other adjustments explained in the Help available from the sidebar. Here is an example:<br />
[[Image:news.gif |200px]]<br />
<br />
It is nice to add a discussion question or two. The format for this is:<br />
<br />
DISCUSSION:<br />
<br />
(1) Do you think this Templet will be helpfull?<br />
<br />
(2) What have I left out?</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=How_to_submit_a_new_article_or_edit_an_existing_article&diff=331How to submit a new article or edit an existing article2005-05-31T13:42:17Z<p>Laurie Snell: </p>
<hr />
<div>To modify a page choose "edit" from the top of the page and make the desired changes. Then choose "Show preview" from the bottom of the page. If you are satified with your changes choose "Save" at the bottom of the page. In the Summary box indicate the type of change you made. You can modify the content of the article or add discussion questions that you might think of while reading the artice. For additional help in editing a page, including how to add pictures, links, special characters, etc., choose "Help" from the side box. <br />
<br />
To add a new article, choose a name for the article. This can be the name used by the news media or a name chosen by you. Then from the Main Page choose the most recent Chance News. Using "edit" add the name for your article to the list of the previous items. Note that we do not put a period at the end of the name. Then click on your title and a blank page will turn up. Choose edit from the top of this page and add the source of your article and your comments about it. The page [[Template]] provides examples of formating that you might meet in adding your article.<br />
<br />
The "discussion" at the top of a page allows can be used to add comments related to that page. The discussion page for an article can be used for comments about the article, for the current Chance News page to suggest additional articles, and for the Main page to comment on the Chance Wiki itself.<br />
<br />
Copyright. Since, in most cases, we are doing a critical analysis of an article, fair use should allow us to make reasonable quotes, graphics, images etc. from the article without the permission of the copyright owner. You can read one lawyer's interpretation of fair use as it applies to Chance News [http://www.dartmouth.edu/~chance/Fair_Use/fair.html here]. Of course we should be sure to give the source of anything we use. When you upload an image you will be asked to indicate if you are doing it under fair use or you have permission from the copyright owner and also to give the source. This information will be made known to the reader by clicking on the image. <br />
<br />
Good luck and remember it will be easier next time!</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Templet&diff=13115Templet2005-05-31T13:37:46Z<p>Laurie Snell: Templet</p>
<hr />
<div>Mix math and medicine and create confusion<br><br />
New York Times, April 26, 2005, F 11<br><br />
Richard Friedman, M.D<br />
<br />
This article provides an interesting exchange between a doctor (Doctor Friedman) and a statistician (Judith Singer).<br />
<br />
(The break marks are necessary because Wiki only make a new line when it sees a blank spaces. Do not leave a space before typing a line. If you do you will get a box around the line!)<br />
<br />
To make a link to a website, for example to the [http://www.dartmouth.edu/~chance Chance Website] Website, start with the URL, add a space, and add name of the website. Put this whole thing in brackets. <br />
<br />
There are two ways to indent a quotation. The first is to indent each line using :, ::, ::: depending on how much you want to indent it.<br />
<br />
::We've heard that a million monkeys at a million keyboards could <br />
::produce the complete works of Shakespeare.Now, thanks to the<br />
::Internet, we know that is not true. ~ Robert Wilensky<br />
<br />
The other is to use the web blockqote.<br />
<blockquote><br />
We've heard that a million monkeys at a million keyboards could produce the complete works of Shakespeare. Now, thanks to the<br />
Internet, we know that is not true. ~ Robert Wilensky<br />
</blockquote><br />
<br />
There are two ways to add images. If you have a URL for the image you can just give this without any brackets. For example:<br />
<br />
<center> http://www.dartmouth.edu/~chance/wikividios/primeWSJ.jpg</center><br />
<br />
The other method is to upload the image. For this you have to login and use the "Upload file" that appears on the sidebar after you register. If you use this method you can adjust the size and make other adjustments explained in the Help available from the sidebar. Here is an example:<br />
[[Image:news.gif |200px]]<br />
<br />
It is nice to add a discussion question or two. The format for this is:<br />
<br />
DISCUSSION:<br />
<br />
(1) Do you think this Templet will be helpfull?<br />
<br />
(2) What have I left out?</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Templet&diff=328Templet2005-05-31T13:26:36Z<p>Laurie Snell: </p>
<hr />
<div>Mix math and medicine and create confusion<br><br />
New York Times, April 26, 2005, F 11<br><br />
Richard Friedman, M.D<br />
<br />
This article provides an interesting exchange between a doctor (Doctor Friedman) and a statistician (Judith Singer).<br />
<br />
(The break marks are necessary because Wiki only make a new line when it sees a blank spaces. Do not leave a space before typing a line. If you do you will get a box around the line!)<br />
<br />
To make a link to a website, for example to the [http://www.dartmouth.edu/~chance Chance Website] Website, start with the URL, add a space, and add name of the website. Put this whole thing in brackets. <br />
<br />
There are two ways to indent a quotation. The first is to indent each line using :, ::, ::: depending on how much you want to indent it.<br />
<br />
::We've heard that a million monkeys at a million keyboards could <br />
::produce the complete works of Shakespeare.Now, thanks to the<br />
::Internet, we know that is not true. ~ Robert Wilensky<br />
<br />
The other is to use the web blockqote.<br />
<blockquote><br />
We've heard that a million monkeys at a million keyboards could produce the complete works of Shakespeare. Now, thanks to the<br />
Internet, we know that is not true. ~ Robert Wilensky<br />
</blockquote><br />
<br />
There are two ways to add images. If you have a URL for the image you can just give this without any brackets. For example:<br />
<br />
<center> http://www.dartmouth.edu/~chance/wikividios/primeWSJ.jpg</center></div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Templet&diff=327Templet2005-05-31T13:18:32Z<p>Laurie Snell: </p>
<hr />
<div>Mix math and medicine and create confusion<br><br />
New York Times, April 26, 2005, F 11<br><br />
Richard Friedman, M.D<br />
<br />
This article provides an interesting exchange between a doctor (Doctor Friedman) and a statistician (Judith Singer).<br />
<br />
(The break marks are necessary because Wiki only make a new line when it sees a blank spaces. Do not leave a space before typing a line. If you do you will get a box around the line!)<br />
<br />
To make a link to a website, for example to the [http://www.dartmouth.edu/~chance Chance Website] Website, start with the URL, add a space, and add name of the website. Put this whole thing in brackets. <br />
<br />
There are two ways to indent a quotation. The first is to indent each line using :, ::, ::: depending on how much you want to indent it.<br />
<br />
::We've heard that a million monkeys at a million keyboards could <br />
::produce the complete works of Shakespeare.Now, thanks to the<br />
::Internet, we know that is not true. ~ Robert Wilensky<br />
<br />
The other is to use the web blockqote.<br />
<blockquote><br />
We've heard that a million monkeys at a million keyboards could produce the complete works of Shakespeare. Now, thanks to the<br />
Internet, we know that is not true. ~ Robert Wilensky<br />
</blockquote><br />
<br />
There are two ways to add images. If you have a URL for the image you can just give this without any brackets. For example:</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Templet&diff=326Templet2005-05-29T18:33:35Z<p>Laurie Snell: </p>
<hr />
<div>Mix math and medicine and create confusion<br><br />
New York Times, April 26, 2005, F 11<br><br />
Richard Friedman, M.D<br />
<br />
This article provides an interesting exchange between a doctor (Doctor Friedman) and a statistician (Judith Singer).<br />
<br />
(The break marks are necessary because Wiki only make a new line when it sees a blank spaces. Do not leave a space before typing a line. If you do you will get a box around the line!)<br />
<br />
To make a link to a website, for example to the [http://www.dartmouth.edu/~chance Chance Website] Website, start with the URL, add a space, and add name of the website. Put this whole thing in brackets. <br />
<br />
There are two ways to indent a quotation. The first is to indent each line using :, ::, ::: depending on how much you want to indent it.<br />
<br />
::We've heard that a million monkeys at a million keyboards could <br />
::produce the complete works of Shakespeare.Now, thanks to the<br />
::Internet, we know that is not true. ~ Robert Wilensky<br />
<br />
The other is to use the web blockqote.<br />
<blockquote><br />
We've heard that a million monkeys at a million keyboards could produce the complete works of Shakespeare. Now, thanks to the<br />
Internet, we know that is not true. ~ Robert Wilensky<br />
</blockquote></div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Templet&diff=325Templet2005-05-29T18:17:07Z<p>Laurie Snell: </p>
<hr />
<div>Mix math and medicine and create confusion<br><br />
New York Times, April 26, 2005, F 11<br><br />
Richard Friedman, M.D<br />
<br />
This article provides an interesting exchange between a doctor (Doctor Friedman) and a statistician (Judith Singer).<br />
<br />
(The break marks are necessary because Wiki only make a new line when it sees a blank spaces. Do not leave a space before typing a line. If you do you will get a box around the line!)<br />
<br />
There are two ways to indent a quotation. The first is to indent each line using :, ::, ::: depending on how much you want to indent it.<br />
<br />
::We've heard that a million monkeys at a million keyboards could <br />
::produce the complete works of Shakespeare.Now, thanks to the<br />
::Internet, we know that is not true. ~ Robert Wilensky<br />
<br />
The other is to use the web blockqote.<br />
<blockquote><br />
We've heard that a million monkeys at a million keyboards could produce the complete works of Shakespeare. Now, thanks to the<br />
Internet, we know that is not true. ~ Robert Wilensky<br />
</blockquote></div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Templet&diff=324Templet2005-05-29T17:58:56Z<p>Laurie Snell: </p>
<hr />
<div>Mix math and medicine and create confusion<br><br />
New York Times, April 26, 2005, F 11<br><br />
Richard Friedman, M.D<br />
<br />
This article provides an interesting exchange between a doctor (Doctor Friedman) and a statistician (Judith Singer).<br />
<br />
(The break marks are necessary because Wiki only make a new line when it sees a blank spaces. Do not leave a space before typing a line. If you do you will get a box around the line!)<br />
<br />
<br />
::We've heard that a million monkeys at a million keyboards could <br />
::produce the complete works of Shakespeare.Now, thanks to the<br />
::Internet, we know that is not true. ~ Robert Wilensky<br />
<br />
<br />
<br />
<br />
<br />
<br />
<blockquote><br />
We've heard that a million monkeys at a million keyboards could produce the complete works of Shakespeare. Now, thanks to the<br />
Internet, we know that is not true. ~ Robert Wilensky<br />
</blockquote></div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Templet&diff=323Templet2005-05-29T17:52:27Z<p>Laurie Snell: </p>
<hr />
<div>Mix math and medicine and create confusion<br><br />
New York Times, April 26, 2005, F 11<br><br />
Richard Friedman, M.D<br />
<br />
This article provides an interesting exchange between a doctor (Doctor Friedman) and a statistician (Judith Singer).<br />
<br />
(The break marks are necessary because Wiki only make a new line when it sees a blank spaces. Do not leave a space before typing a line. If you do you will get a box around the line!)</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Templet&diff=322Templet2005-05-29T15:49:38Z<p>Laurie Snell: </p>
<hr />
<div>Mix math and medicine and create confusion<br><br />
New York Times, April 26, 2005, F 11<br><br />
Richard Friedman, M.D<br />
<br />
(The break marks are necessary because Wiki only make a new line when it sees a blank spaces.)<br />
<br />
This article provides an interesting exchange between a doctor (Doctor Friedman) and a statistician (Judith Singer).<br />
<br />
(do not leave a space before typing a line. If you do you will get a box around your line!)<br />
<br />
to be continued</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=How_to_submit_a_new_article_or_edit_an_existing_article&diff=329How to submit a new article or edit an existing article2005-05-29T15:38:35Z<p>Laurie Snell: </p>
<hr />
<div>To modify a page choose "edit" from the top of the page and make the desired changes. Then choose "Show preview" from the bottom of the page. If you are satified with your changes choose "Save" at the bottom of the page. In the Summary box indicate the type of change you made. You can modify the content of the article or add discussion questions that you might think of while reading the artice. For additional help in editing a page, including how to add pictures, links, special characters, etc., choose "Help" from the side box. <br />
<br />
To add a new article, choose a name for the article. This can be the name used by the news media or a name chosen by you. Then from the Main Page choose the most recent Chance News. Using "edit" add the name for your article to the list of the previous items. Note that we do not put a period at the end of the name. Then click on your title and a blank page will turn up. Choose edit from the top of this page and add the source of your article and your comments about it. The page [[Templet]] provides examples of formating that you might meet in adding your article.<br />
<br />
The "discussion" at the top of a page allows can be used to add comments related to that page. The discussion page for an article can be used for comments about the article, for the current Chance News page to suggest additional articles, and for the Main page to comment on the Chance Wiki itself.<br />
<br />
Copyright. Since, in most cases, we are doing a critical analysis of an article, fair use should allow us to make reasonable quotes, graphics, images etc. from the article without the permission of the copyright owner. You can read one lawyer's interpretation of fair use as it applies to Chance News [http://www.dartmouth.edu/~chance/Fair_Use/fair.html here]. Of course we should be sure to give the source of anything we use. When you upload an image you will be asked to indicate if you are doing it under fair use or you have permission from the copyright owner and also to give the source. This information will be made known to the reader by clicking on the image. <br />
<br />
Good luck and remember it will be easier next time!</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=How_to_submit_a_new_article_or_edit_an_existing_article&diff=321How to submit a new article or edit an existing article2005-05-29T15:27:55Z<p>Laurie Snell: </p>
<hr />
<div>To modify a page choose "edit" from the top of the page and make the desired changes. Then choose "Show preview" from the bottom of the page. If you are satified with your changes choose "Save" at the bottom of the page. In the Summary box indicate the type of change you made. You can modify the content of the article or add discussion questions that you might think of while reading the artice. For additional help in editing a page, including how to add pictures, links, special characters, etc., choose "Help" from the side box. <br />
<br />
To add a new article, choose a name for the article. This can be the name used by the news media or a name chosen by you. Then from the Main Page choose the most recent Chance News. Using "edit" add the name for your article to the list of the previous items. Note that we do not put a period at the end of the name. Then click on your title and a blank page will turn up. Choose edit from the top of this page and add the source of your article and your comments about it. Go [[here]] for a templet for a new article. <br />
<br />
The "discussion" at the top of a page allows can be used to add comments related to that page. The discussion page for an article can be used for comments about the article, for the current Chance News page to suggest additional articles, and for the Main page to comment on the Chance Wiki itself.<br />
<br />
Copyright. Since, in most cases, we are doing a critical analysis of an article, fair use should allow us to make reasonable quotes, graphics, images etc. from the article without the permission of the copyright owner. You can read one lawyer's interpretation of fair use as it applies to Chance News [http://www.dartmouth.edu/~chance/Fair_Use/fair.html here]. Of course we should be sure to give the source of anything we use. When you upload an image you will be asked to indicate if you are doing it under fair use or you have permission from the copyright owner and also to give the source. This information will be made known to the reader by clicking on the image. <br />
<br />
Good luck and remember it will be easier next time!</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=How_to_submit_a_new_article_or_edit_an_existing_article&diff=320How to submit a new article or edit an existing article2005-05-29T15:19:00Z<p>Laurie Snell: </p>
<hr />
<div>To modify a page choose "edit" from the top of the page and make the desired changes. Then choose "Show preview" from the bottom of the page. If you are satified with your changes choose "Save" at the bottom of the page. In the Summary box indicate the type of change you made. You can modify the content of the article or add discussion questions that you might think of while reading the artice.<br />
<br />
To add a new article, choose a name for the article. This can be the name used by the news media or a name chosen by you. Then from the Main Page choose the most recent Chance News. Using "edit" add the name for your article to the list of the previous items. Note that we do not put a period at the end of the name. Then click on your title and a blank page will turn up. Choose edit from the top of this page and add the source of your article and your comments about it. Go [[here]] for a templet of a new article.<br />
<br />
For additional help in editing a page, including how to add pictures, links, special characters, etc., choose "Help" from the side box. You might also want to use an excisting article as a guide.<br />
<br />
The "discussion" at the top of a page allows can be used to add comments related to that page. The discussion page for an article can be used for comments about the article, for the current Chance News page to suggest additional articles, and for the Main page to comment on the Chance Wiki itself.<br />
<br />
Copyright. Since, in most cases, we are doing a critical analysis of an article, fair use should allow us to make reasonable quotes, graphics, images etc. from the article without the permission of the copyright owner. You can read one lawyer's interpretation of fair use as it applies to Chance News [http://www.dartmouth.edu/~chance/Fair_Use/fair.html here]. Of course we should be sure to give the source of anything we use. When you upload an image you will be asked to indicate if you are doing it under fair use or you have permission from the copyright owner and also to give the source. This information will be made known to the reader by clicking on the image. <br />
<br />
Good luck and remember it will be easier next time!</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Mix_math_and_medicine_and_create_confusion&diff=545Mix math and medicine and create confusion2005-05-28T19:20:18Z<p>Laurie Snell: </p>
<hr />
<div>Mix math and medicine and create confusion<br><br />
New York Times, April 26, 2005, F 11<br><br />
Richard Friedman, M.D<br />
<br />
This article provides an interesting exchange between a doctor (Doctor Friedman) and a statistician (Judith Singer). We give the entire exchange as presenting in this article by Dr. Friedman. <br />
<blockquote><br />
Patients may not know it, but there are two questions that make doctors cringe. The most common is, If you were me, which treatment option would you pick? The tougher one is, What are the chances that this treatment will help me?'<br />
</blockquote><br />
<blockquote><br />
Both questions cut to the heart of medical decision making and involve assessing risk and probability, which does not come naturally to many people.<br />
</blockquote><br />
<blockquote><br />
For example, a depressed patient told me she had read that the chances were 60 percent that she would respond to the antidepressant I had prescribed for her. <br />
</blockquote><br />
<blockquote><br />
"That means that 60 percent of the time I will feel better on this, right?" she asked. <br />
</blockquote><br />
<blockquote><br />
Well, not exactly. I explained that if 10 people with a depression just like hers walked into my office, about 6 would be expected to respond to that antidepressant. <br />
</blockquote><br />
<blockquote><br />
But the statistics, I told her, referred to a large sample, not an individual. She would either improve with this treatment or she would not, I said, but she shouldn't worry because we would keep trying until we found a treatment that worked. <br />
</blockquote><br />
<blockquote><br />
"You mean my chances of getting better are really only 50 percent?" she asked with dismay. <br />
</blockquote><br />
<blockquote><br />
Dr. Judith D. Singer, a statistician and professor at the Graduate School of Education at Harvard, explained "You and your patient are confusing two different concepts. The number of possible outcomes -- in her case either responding or not responding to an antidepressant -- has nothing to do with the actual probability of either outcome happening."<br />
</blockquote><br />
<blockquote><br />
For example, Dr. Singer said, "Either a woman is pregnant or not. She can't be a little pregnant. But that doesn't mean that she has a 50 percent probability of being pregnant." <br />
</blockquote><br />
<blockquote><br />
A woman who takes a fertility pill may stand a much higher chance of actually getting pregnant than if she goes without it. If my patient was typical of the subjects in the clinical trial she read about, Dr. Singer said, "she is more likely than not to get better on that antidepressant."<br />
<br />
DISCUSSION QUESTIONS:<br />
<br />
(1) The doctor explained 60% chance of a response from the antidepressant as "If 10 people with a depression just like hers walked into my office, about 6 would be expected to respond to that antidepressant. The statistician's explanation was: If my patient was typical of the subjects in the clinical trial she read about, she is more likely than not to get the better on that antidepressant. What are the pros and cons of these explanations? How would you answer the question?<br />
<br />
(2) If your doctor would answer one of the two questions that make doctors cringe, which would you prefer? Why?</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Mix_math_and_medicine_and_create_confusion&diff=318Mix math and medicine and create confusion2005-05-28T19:07:06Z<p>Laurie Snell: </p>
<hr />
<div>Mix math and medine and create confusion<br><br />
New York Times, April 26, 2005, F 11<br><br />
Richard Friedman, M.D<br />
<br />
This article provides an interesting exchange between a doctor (Doctor Friedman) and a statistician (Judith Singer). We give the entire exchange as presenting in this article by Dr. Friedman. <br />
<blockquote><br />
Patients may not know it, but there are two questions that make doctors cringe. The most common is, If you were me, which treatment option would you pick? The tougher one is, What are the chances that this treatment will help me?'<br />
</blockquote><br />
<blockquote><br />
Both questions cut to the heart of medical decision making and involve assessing risk and probability, which does not come naturally to many people.<br />
</blockquote><br />
<blockquote><br />
For example, a depressed patient told me she had read that the chances were 60 percent that she would respond to the antidepressant I had prescribed for her. <br />
</blockquote><br />
<blockquote><br />
"That means that 60 percent of the time I will feel better on this, right?" she asked. <br />
</blockquote><br />
<blockquote><br />
Well, not exactly. I explained that if 10 people with a depression just like hers walked into my office, about 6 would be expected to respond to that antidepressant. <br />
</blockquote><br />
<blockquote><br />
But the statistics, I told her, referred to a large sample, not an individual. She would either improve with this treatment or she would not, I said, but she shouldn't worry because we would keep trying until we found a treatment that worked. <br />
</blockquote><br />
<blockquote><br />
"You mean my chances of getting better are really only 50 percent?" she asked with dismay. <br />
</blockquote><br />
<blockquote><br />
Dr. Judith D. Singer, a statistician and professor at the Graduate School of Education at Harvard, explained "You and your patient are confusing two different concepts. The number of possible outcomes -- in her case either responding or not responding to an antidepressant -- has nothing to do with the actual probability of either outcome happening."<br />
</blockquote><br />
<blockquote><br />
For example, Dr. Singer said, "Either a woman is pregnant or not. She can't be a little pregnant. But that doesn't mean that she has a 50 percent probability of being pregnant." <br />
</blockquote><br />
<blockquote><br />
A woman who takes a fertility pill may stand a much higher chance of actually getting pregnant than if she goes without it. If my patient was typical of the subjects in the clinical trial she read about, Dr. Singer said, "she is more likely than not to get better on that antidepressant."<br />
<br />
DISCUSSION QUESTIONS:<br />
<br />
(1) The doctor explained 60% chance of a response from the antidepressent as "If 10 people with a drepression just like hers walked into my office, about 6 would be expected to respond to that antidepressant. The satisticians explanation was: If my patient was typical of the subjects in the clinical trial she read about, she is more likely than not to get the better on that antidepresssant. What are the pros and cons of these explanations? How would you answer the question?<br />
<br />
(2) If your doctor would answer one of the two questions that make doctors cringe, which would you prefer? Why?</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Mix_math_and_medicine_and_create_confusion&diff=317Mix math and medicine and create confusion2005-05-28T18:20:18Z<p>Laurie Snell: </p>
<hr />
<div>Mix math and medine and create confusion<br><br />
New York Times, April 26, 2005, F 11<br><br />
Richard Friedman, M.D<br />
<br />
This article provides an interesting exchange between a doctor (Doctor Friedman) and a statistician (Judith Singer). We give the entire exchange as presenting in this article by Dr. Friedman. <br />
<blockquote><br />
Patients may not know it, but there are two questions that make doctors cringe. The most common is, If you were me, which treatment option would you pick? The tougher one is, What are the chances that this treatment will help me?'<br />
</blockquote><br />
<blockquote><br />
Both questions cut to the heart of medical decision making and involve assessing risk and probability, which does not come naturally to many people.<br />
</blockquote><br />
<blockquote><br />
For example, a depressed patient told me she had read that the chances were 60 percent that she would respond to the antidepressant I had prescribed for her. <br />
</blockquote><br />
<blockquote><br />
"That means that 60 percent of the time I will feel better on this, right?" she asked. <br />
</blockquote><br />
<blockquote><br />
Well, not exactly. I explained that if 10 people with a depression just like hers walked into my office, about 6 would be expected to respond to that antidepressant. <br />
</blockquote><br />
<blockquote><br />
But the statistics, I told her, referred to a large sample, not an individual. She would either improve with this treatment or she would not, I said, but she shouldn't worry because we would keep trying until we found a treatment that worked. <br />
</blockquote><br />
<blockquote><br />
"You mean my chances of getting better are really only 50 percent?" she asked with dismay. <br />
</blockquote><br />
<blockquote><br />
Dr. Judith D. Singer, a statistician and professor at the Graduate School of Education at Harvard, explained "You and your patient are confusing two different concepts. The number of possible outcomes -- in her case either responding or not responding to an antidepressant -- has nothing to do with the actual probability of either outcome happening."<br />
</blockquote><br />
<blockquote><br />
For example, Dr. Singer said, "Either a woman is pregnant or not. She can't be a little pregnant. But that doesn't mean that she has a 50 percent probability of being pregnant." <br />
</blockquote><br />
<blockquote><br />
A woman who takes a fertility pill may stand a much higher chance of actually getting pregnant than if she goes without it. If my patient was typical of the subjects in the clinical trial she read about, Dr. Singer said, "she is more likely than not to get better on that antidepressant."</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Mix_math_and_medicine_and_create_confusion&diff=316Mix math and medicine and create confusion2005-05-28T18:04:21Z<p>Laurie Snell: </p>
<hr />
<div>Mix math and medine and create confusion<br><br />
New York Times, April 26, 2005, F 11<br><br />
Richard Friedman, M.D<br />
<br />
This article provides an interesting exchange between a doctor (Doctor Friedman) and a statistician (Judith Singer). We give the entire exchange as presenting in this article by Dr. Friedman. <br />
<blockquote><br />
Patients may not know it, but there are two questions that make doctors cringe. The most common is, If you were me, which treatment option would you pick? The tougher one is, What are the chances that this treatment will help me?'<br />
</blockquote><br />
<blockquote><br />
Both questions cut to the heart of medical decision making and involve assessing risk and probability, which does not come naturally to many people.<br />
</blockquote><br />
<blockquote><br />
For example, a depressed patient told me she had read that the chances were 60 percent that she would respond to the antidepressant I had prescribed for her. <br />
</blockquote><br />
<blockquote><br />
That means that 60 percent of the time I will feel better on this, right? she asked. <br />
</blockquote><br />
<blockquote><br />
Well, not exactly. I explained that if 10 people with a depression just like hers walked into my office, about 6 would be expected to respond to that antidepressant. <br />
</blockquote><br />
<blockquote><br />
But the statistics, I told her, referred to a large sample, not an individual. She would either improve with this treatment or she would not, I said, but she shouldn't worry because we would keep trying until we found a treatment that worked. <br />
</blockquote><br />
<blockquote><br />
You mean my chances of getting better are really only 50 percent? she asked with dismay. <br />
</blockquote><br />
<blockquote><br />
Dr. Judith D. Singer, a statistician and professor at the Graduate School of Education at Harvard, explained: You and your patient are confusing two different concepts. The number of possible outcomes -- in her case either responding or not responding to an antidepressant -- has nothing to do with the actual probability of either outcome happening.' <br />
</blockquote><br />
<blockquote><br />
For example, Dr. Singer said, Either a woman is pregnant or not. She can't be a little pregnant. But that doesn't mean that she has a 50 percent probability of being pregnant. <br />
</blockquote><br />
<blockquote><br />
A woman who takes a fertility pill may stand a much higher chance of actually getting pregnant than if she goes without it.'<br />
</blockquote><br />
<blockquote<br />
If my patient was typical of the subjects in the clinical trial she read about, Dr. Singer said, she is more likely than not to get better on that antidepressant.'</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Mix_math_and_medicine_and_create_confusion&diff=315Mix math and medicine and create confusion2005-05-28T18:03:15Z<p>Laurie Snell: </p>
<hr />
<div>Mix math and medine and create confusion<br><br />
New York Times, April 26, 2005, F 11<br><br />
Richard Friedman, M.D<br />
<br />
This article provides an interesting exchange between a doctor (Doctor Friedman) and a statistician (Judith Singer). We give the entire exchange as presenting by Dr. Friedman in this article.<br />
<blockquote><br />
Patients may not know it, but there are two questions that make doctors cringe. The most common is, If you were me, which treatment option would you pick? The tougher one is, What are the chances that this treatment will help me?'<br />
</blockquote><br />
<blockquote><br />
Both questions cut to the heart of medical decision making and involve assessing risk and probability, which does not come naturally to many people.<br />
</blockquote><br />
<blockquote><br />
For example, a depressed patient told me she had read that the chances were 60 percent that she would respond to the antidepressant I had prescribed for her. <br />
</blockquote><br />
<blockquote><br />
That means that 60 percent of the time I will feel better on this, right? she asked. <br />
</blockquote><br />
<blockquote><br />
Well, not exactly. I explained that if 10 people with a depression just like hers walked into my office, about 6 would be expected to respond to that antidepressant. <br />
</blockquote><br />
<blockquote><br />
But the statistics, I told her, referred to a large sample, not an individual. She would either improve with this treatment or she would not, I said, but she shouldn't worry because we would keep trying until we found a treatment that worked. <br />
</blockquote><br />
<blockquote><br />
You mean my chances of getting better are really only 50 percent? she asked with dismay. <br />
</blockquote><br />
<blockquote><br />
Dr. Judith D. Singer, a statistician and professor at the Graduate School of Education at Harvard, explained: You and your patient are confusing two different concepts. The number of possible outcomes -- in her case either responding or not responding to an antidepressant -- has nothing to do with the actual probability of either outcome happening.' <br />
</blockquote><br />
<blockquote><br />
For example, Dr. Singer said, Either a woman is pregnant or not. She can't be a little pregnant. But that doesn't mean that she has a 50 percent probability of being pregnant. <br />
</blockquote><br />
<blockquote><br />
A woman who takes a fertility pill may stand a much higher chance of actually getting pregnant than if she goes without it.'<br />
</blockquote><br />
<blockquote<br />
If my patient was typical of the subjects in the clinical trial she read about, Dr. Singer said, she is more likely than not to get better on that antidepressant.'</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Mix_math_and_medicine_and_create_confusion&diff=314Mix math and medicine and create confusion2005-05-28T18:02:46Z<p>Laurie Snell: </p>
<hr />
<div>Mix math and medine and create confusion<br><br />
New York Times, April 26, 2005, F 11<br><br />
Richard Friedman, M.D<br />
<br />
This article provides an interesting exchange between a doctor (Doctor Friedman) and a statistician Judith Singer). We give the entire exchange as presenting by Dr. Friedman in this article.<br />
<blockquote><br />
Patients may not know it, but there are two questions that make doctors cringe. The most common is, If you were me, which treatment option would you pick? The tougher one is, What are the chances that this treatment will help me?'<br />
</blockquote><br />
<blockquote><br />
Both questions cut to the heart of medical decision making and involve assessing risk and probability, which does not come naturally to many people.<br />
</blockquote><br />
<blockquote><br />
For example, a depressed patient told me she had read that the chances were 60 percent that she would respond to the antidepressant I had prescribed for her. <br />
</blockquote><br />
<blockquote><br />
That means that 60 percent of the time I will feel better on this, right? she asked. <br />
</blockquote><br />
<blockquote><br />
Well, not exactly. I explained that if 10 people with a depression just like hers walked into my office, about 6 would be expected to respond to that antidepressant. <br />
</blockquote><br />
<blockquote><br />
But the statistics, I told her, referred to a large sample, not an individual. She would either improve with this treatment or she would not, I said, but she shouldn't worry because we would keep trying until we found a treatment that worked. <br />
</blockquote><br />
<blockquote><br />
You mean my chances of getting better are really only 50 percent? she asked with dismay. <br />
</blockquote><br />
<blockquote><br />
Dr. Judith D. Singer, a statistician and professor at the Graduate School of Education at Harvard, explained: You and your patient are confusing two different concepts. The number of possible outcomes -- in her case either responding or not responding to an antidepressant -- has nothing to do with the actual probability of either outcome happening.' <br />
</blockquote><br />
<blockquote><br />
For example, Dr. Singer said, Either a woman is pregnant or not. She can't be a little pregnant. But that doesn't mean that she has a 50 percent probability of being pregnant. <br />
</blockquote><br />
<blockquote><br />
A woman who takes a fertility pill may stand a much higher chance of actually getting pregnant than if she goes without it.'<br />
</blockquote><br />
<blockquote<br />
If my patient was typical of the subjects in the clinical trial she read about, Dr. Singer said, she is more likely than not to get better on that antidepressant.'</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Mix_math_and_medicine_and_create_confusion&diff=313Mix math and medicine and create confusion2005-05-28T17:55:37Z<p>Laurie Snell: </p>
<hr />
<div>Mix math and medine and create confusion<br><br />
New York Times, April 26, 2005, F 11<br><br />
Richard Friedman, M.D<br />
<br />
This article provides an interesting exchange between a doctor (Doctor Friedman) and a statistician Judith Singer). We give the entire exchange as presenting by Dr. Friedman in this article.<br />
<blockquote><br />
Patients may not know it, but there are two questions that make doctors cringe. The most common is, If you were me, which treatment option would you pick? The tougher one is, What are the chances that this treatment will help me?'<br />
</blockquote><br />
<blockquote><br />
Both questions cut to the heart of medical decision making and involve assessing risk and probability, which does not come naturally to many people.<br />
</blockquote><br />
<blockquote><br />
For example, a depressed patient told me she had read that the chances were 60 percent that she would respond to the antidepressant I had prescribed for her. <br />
</blockquote><br />
<blockquote><br />
That means that 60 percent of the time I will feel better on this, right? she asked. <br />
</blockquote><br />
<blockquote><br />
Well, not exactly. I explained that if 10 people with a depression just like hers walked into my office, about 6 would be expected to respond to that antidepressant. <br />
</blockquote><br />
<blockquote><br />
But the statistics, I told her, referred to a large sample, not an individual. She would either improve with this treatment or she would not, I said, but she shouldn't worry because we would keep trying until we found a treatment that worked. <br />
</blockquote><br />
<blockquote><br />
You mean my chances of getting better are really only 50 percent? she asked with dismay. <br />
</blockquote><br />
<blockquote><br />
Dr. Judith D. Singer, a statistician and professor at the Graduate School of Education at Harvard, explained: You and your patient are confusing two different concepts. The number of possible outcomes -- in her case either responding or not responding to an antidepressant -- has nothing to do with the actual probability of either outcome happening.' <br />
</blockquote><br />
<blockquote><br />
For example, Dr. Singer said, Either a woman is pregnant or not. She can't be a little pregnant. But that doesn't mean that she has a 50 percent probability of being pregnant. <br />
</blockquote<br />
<blockquote><br />
A woman who takes a fertility pill may stand a much higher chance of actually getting pregnant than if she goes without it.'<br />
</blockquote><br />
<blockquote<br />
If my patient was typical of the subjects in the clinical trial she read about, Dr. Singer said, she is more likely than not to get better on that antidepressant.'</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Mix_math_and_medicine_and_create_confusion&diff=312Mix math and medicine and create confusion2005-05-28T17:24:57Z<p>Laurie Snell: </p>
<hr />
<div>Mix math and medine and create confusion<br><br />
New York Times, April 26, 2005, F 11<br><br />
Richard Friedman, M.D<br />
<br />
This article provides an interesting exchange between a doctor and a statician. We give the entire exchange as presenting in the article.<br />
<br />
<blockquote><br />
Patients may not know it, but there are two questions that make doctors cringe. The most common is, If you were me, which treatment option would you pick? The tougher one is, What are the chances that this treatment will help me?'<br />
</blockquote><br />
<blockquote><br />
Both questions cut to the heart of medical decision making and involve assessing risk and probability, which does not come naturally to many people.<br />
</blockquote><br />
<blockquote><br />
For example, a depressed patient told me she had read that the chances were 60 percent that she would respond to the antidepressant I had prescribed for her. <br />
</blockquote><br />
<blockquote><br />
That means that 60 percent of the time I will feel better on this, right? she asked. <br />
</blockquote><br />
<blockquote><br />
Well, not exactly. I explained that if 10 people with a depression just like hers walked into my office, about 6 would be expected to respond to that antidepressant. <br />
</blockquote><br />
<blockquote><br />
But the statistics, I told her, referred to a large sample, not an individual. She would either improve with this treatment or she would not, I said, but she shouldn't worry because we would keep trying until we found a treatment that worked. <br />
</blockquote><br />
<blockquote><br />
You mean my chances of getting better are really only 50 percent? she asked with dismay. <br />
</blockquote><br />
<blockquote><br />
Dr. Judith D. Singer, a statistician and professor at the Graduate School of Education at Harvard, explained: You and your patient are confusing two different concepts. The number of possible outcomes -- in her case either responding or not responding to an antidepressant -- has nothing to do with the actual probability of either outcome happening.' <br />
</blockquote><br />
<blockquote><br />
For example, Dr. Singer said, Either a woman is pregnant or not. She can't be a little pregnant. But that doesn't mean that she has a 50 percent probability of being pregnant. <br />
</blockquote<br />
<blockquote><br />
A woman who takes a fertility pill may stand a much higher chance of actually getting pregnant than if she goes without it.'<br />
</blockquote><br />
<blockquote<br />
If my patient was typical of the subjects in the clinical trial she read about, Dr. Singer said, she is more likely than not to get better on that antidepressant.'</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=Chance_News_(April-May_2005)&diff=337Chance News (April-May 2005)2005-05-28T17:14:51Z<p>Laurie Snell: </p>
<hr />
<div>==CONTENTS ==<br />
<br />
*[[A Chance News quotation]]<br />
<br />
*[[Forsooth]]<br />
<br />
*[[Case leads to fight on Jewish representation on juries]]<br />
<br />
*[[Vermont pays heavy war burden]]<br />
<br />
*[[Seven statistical cliches used by baseball anouncers]]<br />
<br />
*[[Numbed by the numbers, when they just don't add up]]<br />
<br />
*[[Dan Rockmore's book: Stalking the Riemann Hypothesis]]<br />
<br />
*[[The powerball lottery suspects fraud, but its the Fortune Cookies ]]<br />
<br />
*[[Red enhances human performance in contests]]<br />
<br />
*[[Mix math and medicine and create confusion]]</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=The_powerball_lottery_suspects_fraud,_but_its_the_Fortune_Cookies&diff=309The powerball lottery suspects fraud, but its the Fortune Cookies2005-05-26T17:33:05Z<p>Laurie Snell: </p>
<hr />
<div>Who needs Giacomo? Bet on the fortune cookie <br><br />
New York Times, May 11, 2005, National desk; Pg 1<br><br />
Jennifer Lee<br />
<br />
This article reports unexpected winnings in the Powerball lottery of March 30, 2006 which the lottery officials thought might be fraudulent but which had a much simpler explanation.<br />
<br />
For the Powerball lottery, a player chooses 5 distinct numbers from 1 to 53, which we will call the "basic numbers." In addition, the player chooses another number between 1 and 42 which we will call the "bonus number." The lottery randomly chooses 5 basic numbers and one bonus number. If your 6 numbers agree with those chosen by the lottery you win the jackpot (a huge amount). If there is more than one jackpot winner, you share the jackpot with the other winners. There are 8 additional prizes that you do not have to share with other winners. For example, if you buy a $1 ticket and your 5 basic numbers match those of the lottery but your bonus number does not you win $100,000.<br />
<br />
When you buy a $1 lottery ticket, for an additional $1, the lottery offers another bet called the "Power Play". For the Power Play, the lottery randomly chooses a number from the numbers 2,3,4,5,5. This number is called the "multiplier". If you make this bet and you win any prize other than the Jackpot, the prize is multiplid by the multiplier. <br />
<br />
On March 30 drawing of the Powerball lottery, 110 players made a $1 bet, choosing as their five basic numbers 22,28,32,33,39 and as their bonus number 40. The lottery chose the same five basic numbers but chose 42 for their bonus number. The lottery chose 5 for the multiplier. 89 of the 110 winners did not choose the Power Play and so each won $100,000. 21 players chose the Power Play and, since the multiplier was 5, they each won $500,000 dollars. Thus the lottery paid out 19.4 million dollars to these winners .Actually they didn't have to pay out this much since on the back of a ticket:, in small print, we read:<br />
<blockquote><br />
In unusual circumstances, the set prize amount may be paid on a pari-mutuel basis, which will be lower than the published prize amounts.<br />
</blockquote> <br />
Evidently the Lottery officials decided not to use this option in this case.<br />
In addition the article states that the Lottery keeps a $25 million reserve for odd situations<br />
<br />
Power ball officials stated that, considering the number of tickets sold in the 29 states, they expected 4 or 5 winners. The article quotes Chuck Strutt, executive director of the Multi-State Lottery Association as saying:<br />
<blockquote><br />
Panic began at 11:30 pm. March 30 when he got a call from a worried staff member. We didn't sleep a lot that nigh. Is there someone trying to cheat the system?<br />
</blockquote><br />
The lottery athorities tried a number of theories about how people choose their numbers. For example many players pick their numbers following a geometric design on the ticket. Nothing worked. But then the first three winners said that they had obtained the numbers from a fortune cookie. With this lead, they just had to find the fortune cookie maker who had the winning numbers. They found that many different brands of fortune cookies come from the same Long Island City factory owned by Wonton Food. This company turns out four million fortune cookes a day, which are delivered to dealers over the entire country. When shown the numbers, Derrick Wong, of Wonton Food, verified that they had used these numbers. The numbers were chosen from a bowl but the company plans to switch to having them chosen by a computer and Derrick plans to start playing the lottery.<br />
<br />
DISCUSSION QUESTIONS:<br />
<br />
(1) The articles says: <br />
<blockquote><br />
Of course, it could have been worse. The 110 had picked the wrong sixth number -- 40, not 42 -- and would have been first-place winners if they did.<br />
</blockquote><br />
<br />
Worst for whom?<br />
<br />
(2) How do you calculate the probability of getting the 5 basic numbers but not the bonus number correct?<br />
<br />
(3) Do you think that the sales of fortune cookies will increase?</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=The_powerball_lottery_suspects_fraud,_but_its_the_Fortune_Cookies&diff=305The powerball lottery suspects fraud, but its the Fortune Cookies2005-05-26T15:14:05Z<p>Laurie Snell: </p>
<hr />
<div>Who needs Giacomo? Bet on the fortune cookie <br><br />
New York Times, May 11, 2005, National desk; Pg 1<br><br />
Jennifer Lee<br />
<br />
This article reports unexpected winnings in the Powerball lottery of March 30, 2006 which the lottery officials thought might be fraudulent but which had a much simpler explanation.<br />
<br />
For the Powerball lottery, a player chooses 5 distinct numbers from 1 to 53, which we will call the "basic numbers." In addition, the player chooses another number between 1 and 42 which we will call the "bonus number." The lottery randomly chooses 5 basic numbers and one bonus number. If your 6 numbers agree with those chosen by the lottery you win the jackpot (a huge amount). If there is more than one jackpot winner, you share the jackpot with the other winners. There are 8 additional prizes that you do not have to share with other winners. For example, if you buy a $1 ticket and your 5 basic numbers match those of the lottery, but your bonus number does not, you win $100,000.<br />
<br />
When you buy a $1 lottery ticket, for an additional $1, the lottery offers another bet called the "Power Play". For the Power Play, the lottery chooses randomly a number from the numbers 2,3,4,5,5. This number is called the multiplier. If you make this bet and you win any prize other than the Jackpot, this prize is multiplid by the multiplier. <br />
<br />
On March 30 drawing of the Powerball lottery, 110 players made a $1 bet, choosing as their five basic numbers 22,28,32,33,39 and as their bonus number 40. The lottery chose the same five basic numbers but chose 42 for their bonus number. They chose 5 for the multiplier. 89 of the 110 winners did not choose the Power Play and so each won $100,000. 21 players chose the Power Play and, since the multiplier was 5, they each won $500,000 dollars. Thus the lottery paid out to these winners 19.4 million dollars. They actually didn't have to pay out this much since we read, in small print, on the back of a ticket:<br />
In unusual circumstances, the set prize amount may be paid on a pari-mutuel basis, which will be lower than the published prize amounts.<br />
</blockquote> <br />
Evidently the Lottery officials decided not to use this option in this case.<br />
In addition the article states that the Lottery keeps a $25 million reserve for odd situations<br />
<br />
Power ball officials stated that, considering the number of tickets sold in the 29 states, they expected 4 or 5 winners. <br />
<br />
The article quotes Chuck Strutt, executive director of the Multi-State Lottery Association as saying:<br />
<blockquote><br />
Panic began at 11:30 pm. March 30 when he got a call from a worried staff member. We didn't sleep a lot that nigh. Is there someone trying to cheat the system?<br />
</blockquote><br />
They tried a number of theories about the way people choose their numbers. For example many players pick their numbers following a geometric design on the ticket. Nothing worked, but then the first three winners said that they had obtained the numbers from a fortune cookie. With this lead, they just had to find the fortune cookie maker who had the winning numbers. They found that many different brands of fortune cookies come from the same Long Island City factory owned by Wonton Food. This company turns out four million fortune cookes a day, which are used by dealers over the entire country. When shown the numbers, Derrick Wong, of Wonton Food, verified that they had used these numbers. The numbers were chosen from a bowl but the company plans to switch to having them chosen by a computer and Derrick plans to start playing the lottery.<br />
<br />
DISCUSSION QUESTIONS:<br />
<br />
(1) The articles says: <br />
<blockquote><br />
Of course, it could have been worse. The 110 had picked the wrong sixth number -- 40, not 42 -- and would have been first-place winners if they did.<br />
</blockquote><br />
<br />
Worst for whom?<br />
<br />
(1) How do you calculate the probability of getting the 5 basic numbers but not the bonus number correct?<br />
<br />
(2) How many tickets would you have to sell to expect about 110 people to get the five basic numbers but not the bonus number correct?<br />
<br />
<br />
<br />
(3) Do you think that the sales of fortune cookies will increase?</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=The_powerball_lottery_suspects_fraud,_but_its_the_Fortune_Cookies&diff=304The powerball lottery suspects fraud, but its the Fortune Cookies2005-05-26T14:44:07Z<p>Laurie Snell: </p>
<hr />
<div>Who needs Giacomo? Bet on the fortune cookie <br><br />
New York Times, May 11, 2005, National desk; Pg 1<br><br />
Jennifer Lee<br />
<br />
This article reports unexpected winnings in the Powerball lottery of March 30, 2006, which the lottery officials thought, might be fraudulent but which had a much simpler explanation.<br />
<br />
For the Powerball lottery, a player chooses 5 distinct numbers from 1 to 53, which we call the "basic numbers." In addition, the player chooses another number between 1 and 42 which we call the "bonus number." The lottery randomly chooses 5 basic numbers and one bonus number. If your 6 numbers agree with those chosen by the lottery you win the jackpot (a huge amount). If there is more than one jackpot winner, you share the jackpot with the other winners. There are 8 additional prizes that you do not have to share with other winners. For example, if you buy a $1 ticket and your 5 basic numbers match those of the lottery, but your bonus number does not, you win $100,000.<br />
<br />
When you buy a $1 lottery ticket, the lottery offers another bet called the "Power Play" for an addition $1. For the Power Play the lottery choose random, called "the multiplier", from the numbers 2,3,4,5,5. If you make this bet, and you win any prize other than the Jackpot, this prize is multiplid by the multiplier. <br />
<br />
On March 30 drawing of the Powerball lottery, 110 players made a $1 bet, choosing as their five basic numbers 22,28,32,33,39 and 40 as their bonus number. The lottery chose the same five basic numbers but chose 42 for their bonus number. They chose 5 for the multiplier. 89 of these players did not choose the Power Play and so they each won $100,000. 21 players did choose the Power Play and, since the lottery chose 5 for the multiplier, they each won $500,000 dollars. Thus the lottery paid out to these winners 19.4 million dollars. They actually didn't have to pay out this much since we read on the back of a ticket:<br />
<blockquote><br />
In unusual circumstances, the set prize amount may be paid on a pari-mutuel basis, which will be lower than the published prize amounts.<br />
</blockquote> <br />
Evidently the Lottery officials decided not to use this option in this case.<br />
In addition the article states that the Lottery keeps a $25 million reserve for odd situations<br />
<br />
Power ball officials stated that, considering the number of tickets sold in the 29 states, they expected 4 or 5 winners. <br />
<br />
The article quotes Chuck Strutt, executive director of the Multi-State Lottery Association as saying:<br />
<blockquote><br />
Panic began at 11:30 pm. March 30 when he got a call from a worried staff member. We didn't sleep a lot that nigh. Is there someone trying to cheat the system?<br />
</blockquote><br />
They tried a number of theories about the way people choose their numbers. For example many players pick their numbers following a geometric designs on the ticket. Nothing worked, but then the first three winners said they had obtained the numbers from a fortune cookie. With this lead they just had to find the fortune cookie maker who had the winning numbers. They found that many different brands of fortune cookies come from the same Long Island City factory owned by Wonton Food. This company turns out four million a day, which are used by dealers over the entire country. When shown the numbers Derrick Wong, of Wonton Food, verified that they had used these numbers. The numbers were chosen from a bowl but the company plans to switch to having them chosen by a computer and Derrick plans to play the lottery.<br />
<br />
DISCUSSION QUESTIONS:<br />
<br />
(1) The articles says: <br />
<blockquote><br />
Of course, it could have been worse. The 110 had picked the wrong sixth number -- 40, not 42 -- and would have been first-place winners if they did.<br />
</blockquote><br />
<br />
Worst for whom?<br />
<br />
(1) How do you calculate the probability of getting the 5 basic numbers but not the bonus number correct?<br />
<br />
(2) How many tickets would you have to sell to expect about 110 people to get the five basic numbers but not the bonus number correct?<br />
<br />
<br />
<br />
(3) Do you think that the sales of fortune cookies will increase?</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=The_powerball_lottery_suspects_fraud,_but_its_the_Fortune_Cookies&diff=303The powerball lottery suspects fraud, but its the Fortune Cookies2005-05-26T13:23:08Z<p>Laurie Snell: </p>
<hr />
<div>Who needs Giacomo? Bet on the fortune cookie <br><br />
New York Times, May 11, 2005, National desk; Pg 1<br><br />
Jennifer Lee<br />
<br />
For the powerball lottery, a player chooses 5 distinct number from 1 to 53 which we will call the basic numbers. In addition the player chooses another number between 1 to 42 which we call the "bonus number". The lottery chooses, at random, 5 basic numbers and a bonus number. If your 6 numbers agree with these you win the jackpot (a huge amount)). If there is more than one jackpot winner you jackpot is shared with the winners .There are 9 additional prizes where you do not have to share with other winners.. For example if you buy a $1 ticket and your 5 basic numbers match those of the lottery, but your bonus number does not match the lotteries bonus number, you get $100,000. <br />
<br />
When you buy a $1 lottery ticket, the lottery offers you for $1 another bet called the "Power Play". For the Power Play the lottery choose random from the numbers 2,3,4,5,5. If you make this bet, and you win, any prize other than the Jackpot, your prize will be mutiplied the number chosen by the lottery. <br />
<br />
On March 30 drawing of the Powerball lottery, 110 players made a $1 bet, choosing as their five basic numbers 22,28,32,33,39 and chose 40 as their bonus number.. The lottery chose the same five basic numbers but chose 42 for their bonus number and they chose 5 for the power play number. 89 of these players did not choose the Power Play and they each won $100,000. 21 players did choose the Power Play and since the lottery chose 5 for the multiplyer, they each won $500,000 dollars. Thus the lottery had to play these players 19.4 million dollars.<br />
<br />
Power ball officials stated that considering the number of tickets sold in the 29 states the expected 4 or 5 winners. The lottery does not publish the number of tickets sold. However, we can estimate this number using the fact that the probability of getting the fire basic numbers correct and not getting the bonus number is 1/120,526,770. Using this you would need to sell about 5.4 million tickets to have an exected value of 4.5 <br />
<br />
The article quotes Chuck Strutt, executive director of the Multi-State Lottery Association as saying:<br />
<blockquote><br />
Panic began at 11:30 pm. March 30 when he got a call from a worred staff member. We didn't sleep a lot that nigh. Is there someone trying to cheat the system?<br />
</blockquote><br />
<br />
Then tried a number of theories about the way people choose their numbers. For example they like geometric designs on the ticket when they pick their numbers. Nothing worked, but their first three winners said they had gotten the numbers from a fortune cookie. With this lead they just had to find the fortune cookie maker who had the winning numbers. The found that many different brands of fortune cookes come from the same Long Island City factory, owned by Wonton Food which turns out four million a day. When shown the numbers Derrick Wong, of Wonton Food verified that they had used these numbers. The numbers were chosen from a bowl but the company plans to switch to having them chosen by a computer.<br />
<br />
The article states that the Lottery keeps a $25 million reserve for odd situations. They also have further protections agains events like this one. On the back of the ticket we read<br />
<blockquote><br />
In unusual circumstances, the set prize amount may be paid on a parimutuel basis which will be lower than the published prize amounts.<br />
</blockquote><br />
Evidently the Lottery officials decided not to use this option in this case.<br />
<br />
DISCUSSION QUESTIONS:<br />
<br />
(1) How do you calculate the probability of getting the 5 basic numbers but not the bonus number correct?<br />
<br />
(2) How many tickets would you have to sell to expect about 110 people to get the five basic numbers but not the bonus number correct?<br />
<br />
(3) (2) Do you think that the sales of fortune cookies will increase?</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=The_powerball_lottery_suspects_fraud,_but_its_the_Fortune_Cookies&diff=300The powerball lottery suspects fraud, but its the Fortune Cookies2005-05-25T18:13:32Z<p>Laurie Snell: </p>
<hr />
<div>Who needs Giacomo? Bet on the fortune cookie <br><br />
New York Times, May 11, 2005, National desk; Pg 1<br><br />
Jennifer Lee<br />
<br />
For the powerball lottery, a player chooses 5 distinct number from 1 to 53 which we will call the basic numbers. In addition the player chooses another number between 1 to 42 which we call the "bonus number". The lottery chooses, at random, 5 basic numbers and a bonus number. If your 6 numbers agree with theese you win the jackpot (a huge amount)). If there is more than one jackpot winner you jackpot is shared with the winners .There are 9 additional prizes where you do not have to share with other winners.. For example if buy a $1 icket and your 5 basic numbers match those of the lottery, but your bonus number does not match the lotteries bonus number you get $100,000. <br />
<br />
When you buy a $1 lottery ticket, the lottery offers you for $1 another bet called the "Power Play". For the Power Play the lottery choose random from the numbers 2,3,4,5,5. If you make this bet, and you win, any prize other than the Jackpot, your prize will be mutiplied the number chosen by the lottery. <br />
<br />
On March 30 drawing of the Powerball lottery, 110 players made a $1 bet, choosing as their five basic numbers 22,28,32,33,39 and chose 40 as their bonus number.. The lottery chose the same five basic numbers but chose 42 for their bonus number and they chose 5 for the power play number. 89 of these players did not choose the Power Play and they each won $100,000. 21 players did choose the Power Play and since the lottery chose 5 for the multiplyer, they each won $500,000 dollars. Thus the lottery had to play these players 19.4 million dollars.<br />
<br />
Power ball officials stated that considering the number of tickets sold in the 29 states the expected 4 or 5 winners. The lottery does not publish the number of tickets sold. However, we can estimate this number using the fact that the probability of getting the fire basic numbers correct and not getting the bonus number is 1/120,526,770. Using this you would need to sell about 5.4 million tickets to have an exected value of 4.5 <br />
<br />
</blockquote><br />
The article quotes Chuck Strutt, executive director of the Multi-State Lottery Association as saying:<br />
<blockquote><br />
Panic began at 11:30 pm. March 30 when he got a call from a worred staff member. We didn't sleep a lot that nigh. Is there someone trying to cheat the system?<br />
</blockquote><br />
<br />
Then tried a number of theories about the way people choose their numbers. For example the like geometric designs on the ticket when they pick their numbers. Nothing worked but their first three winners said they had gotten the numbers from a fortune cookie. With this lead they just had to find the fortune cookie maker who had the winning numbers. The found that many different brands of fortune cookes come from the same Long Island City factory, owned by Wonton Food which turns out four million a day. When shown the numbers Derrick Wong, of Wonton Food verified that they had used these numbers. The numbers were chosen from a boal but the company plans to switch to having them chosen by a computer.<br />
<br />
The article states that the Lottery keeps a $25 million reserve for odd situations. They also have further protections agains events like this one. On the back of the ticket we read<br />
<blockquote><br />
In unusual circumstances, the set prize amount may be paid on a pari-mutual basis which will be lower than the published prize amounts.</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=The_powerball_lottery_suspects_fraud,_but_its_the_Fortune_Cookies&diff=299The powerball lottery suspects fraud, but its the Fortune Cookies2005-05-25T18:05:24Z<p>Laurie Snell: </p>
<hr />
<div>Who needs Giacomo? Bet on the fortune cookie <br><br />
New York Times, May 11, 2005, National desk; Pg 1<br><br />
Jennifer Lee<br />
<br />
For the powerball lottery, a player chooses 5 distinct number from 1 to 53 which we will call the basic numbers. In addition the player chooses another number between 1 to 42 which we call the "bonus number". The lottery chooses, at random, 5 basic numbers and a bonus number. If your 6 numbers agree with theese you win the jackpot (a huge amount)). If there is more than one jackpot winner you jackpot is shared with the winners .There are 9 additional prizes where you do not have to share with other winners.. For example if buy a $1 icket and your 5 basic numbers match those of the lottery, but your bonus number does not match the lotteries bonus number you get $100,000. <br />
<br />
When you buy a $1 lottery ticket, the lottery offers you for $1 another bet called the "Power Play". For the Power Play the lottery choose random from the numbers 2,3,4,5,5. If you make this bet, and you win, any prize other than the Jackpot, your prize will be mutiplied the number chosen by the lottery. <br />
<br />
On March 30 drawing of the Powerball lottery, 110 players made a $1 bet, choosing as their five basic numbers 22,28,32,33,39 and chose 40 as their bonus number.. The lottery chose the same five basic numbers but chose 42 for their bonus number and they chose 5 for the power play number. 89 of these players did not choose the Power Play bet winning $100,000 and 21 players did choose it winning $500,000 dollars. Thus the lottery had to play these players 19.4 million dollars.<br />
<br />
Power ball officials stated that considering the number of tickets sold in the 29 states the expected 4 or 5 winners. The lottery does not publish the number of tickets sold. However, the probability of getting the fire basic numbers correct and not getting the bonus number is 1/120,526,770 so <br />
</blockquote><br />
The article quotes Chuck Strutt, executive director of the Multi-State Lottery Association as saying:<br />
<blockquote><br />
Panic began at 11:30 pm. March 30 when he got a call from a worred staff member. We didn't sleep a lot that nigh. Is there someone trying to cheat the system?<br />
</blockquote><br />
<br />
Then tried a number of theories about the way people choose their numbers. For example the like geometric designs on the ticket when they pick their numbers. Nothing worked but their first three winners said they had gotten the numbers from a fortune cookie. With this lead they just had to find the fortune cookie maker who had the winning numbers. The found that many different brands of fortune cookes come from the same Long Island City factory, owned by Wonton Food which turns out four million a day. When shown the numbers Derrick Wong, of Wonton Food verified that they had used these numbers. The numbers were chosen from a boal but the company plans to switch to having them chosen by a computer.<br />
<br />
The article states that the Lottery keeps a $25 million reserve for odd situations. They also have further protections agains events like this one. On the back of the ticket we read<br />
<blockquote><br />
In unusual circumstances, the set prize amount may be paid on a pari-mutual basis which will be lower than the published prize amounts.</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=The_powerball_lottery_suspects_fraud,_but_its_the_Fortune_Cookies&diff=297The powerball lottery suspects fraud, but its the Fortune Cookies2005-05-25T15:23:21Z<p>Laurie Snell: </p>
<hr />
<div>Who needs Giacomo? Bet on the fortune cookie <br><br />
New York Times, May 11, 2005, National desk; Pg 1<br><br />
Jennifer Lee<br />
<br />
For the powerball lottery, a player chooses 5 distinct number from 1 to 49 which we will call the basic numbers. In addition you choose another number between 1 to 40 which we will call the "bonus number". The lottery chooses, at random, their 5 basic numbers and their bonus number. If your 6 numbers agree with theirs you win the jackpot (a huge amount)). If their are other jackpot winners you share the jackpot with them .There are additional smaller prizes for getting smaller number of matches. For example if buy a $1 icket and your 5 basic numbers match those chosen by the lottery but you do not choose the same bonus number you get $100,000. which you do not have to share with other such winners. When you buy a $1 lottery ticket, the lottery offers you for $1 another bet called the "Power Play". For the Power Play the lottery choose a number at random from the five numbers 2,3,4,5,5. If make this bet, and you win any prize other than the Jackpot, your prize will be mutiplied the number chosen by the lottery. <br />
<br />
On March 30 drawing of the Powerball lottery, 110 players made a $1 bet, choosing as their five basic numbers 22,28,32,33,39 and as their bonus number 40. 21 of these players payed another dollar for the Power Play. The lottery chose the same five basic numbers and 42 for their bonus number and they chose 5 for the power play number. Thus the lottery had to pay 89 of the winners $100,000 and 21 $500,000 dollars for a total of<br />
$19.4 million. <br />
<br />
Power ball officials stated that considering the number of tickets sold in the 29 states the expected 4 or 5 winners. The lottery does not publish the number of tickets sold. However, the probability of getting the fire basic numbers correct and not getting the bonus number is 1/120,526,770 so <br />
</blockquote><br />
The article quotes Chuck Strutt, executive director of the Multi-State Lottery Association as saying:<br />
<blockquote><br />
Panic began at 11:30 pm. March 30 when he got a call from a worred staff member. We didn't sleep a lot that nigh. Is there someone trying to cheat the system?<br />
</blockquote><br />
<br />
Then tried a number of theories about the way people choose their numbers. For example the like geometric designs on the ticket when they pick their numbers. Nothing worked but their first three winners said they had gotten the numbers from a fortune cookie. With this lead they just had to find the fortune cookie maker who had the winning numbers. The found that many different brands of fortune cookes come from the same Long Island City factory, owned by Wonton Food which turns out four million a day. When shown the numbers Derrick Wong, of Wonton Food verified that they had used these numbers. The numbers were chosen from a boal but the company plans to switch to having them chosen by a computer.<br />
<br />
The article states that the Lottery keeps a $25 million reserve for odd situations. They also have further protections agains events like this one. On the back of the ticket we read<br />
<blockquote><br />
In unusual circumstances, the set prize amoount may be paid on a pari-mutual basis which will be lower than the published prize amounts.</div>Laurie Snellhttps://www.causeweb.org/wiki/chance/index.php?title=The_powerball_lottery_suspects_fraud,_but_its_the_Fortune_Cookies&diff=296The powerball lottery suspects fraud, but its the Fortune Cookies2005-05-25T15:20:31Z<p>Laurie Snell: </p>
<hr />
<div>Who needs Giacomo? Bet on the fortune cookie <br><br />
New York Times, May 11, 2005, National desk; Pg 1<br><br />
Jennifer Lee<br />
<br />
For the powerball lottery, a player chooses 5 distinct number from 1 to 49 which we will call the basic numbers. In addition you choose another number between 1 to 40 which we will call the "bonus number". The lottery chooses, at random, their 5 basic numbers and their bonus number. If your 6 numbers agree with theirs you win the jackpot (a huge amount)). If their are other jackpot winners you share the jackpot with them .There are additional smaller prizes for getting smaller number of matches. For example if buy a $1 icket and your 5 basic numbers match those chosen by the lottery but you do not choose the same bonus number you get $100,000. which you do not have to share with other such winners. When you buy a $1 lottery ticket, the lottery offers you for $1 another bet called the "Power Play". For the Power Play the lottery choose a number at random from the five numbers 2,3,4,5,5. If make this bet, and you win any prize other than the Jackpot, your prize will be mutiplied the number chosen by the lottery. <br />
<br />
On March 30 drawing of the Powerball lottery, 110 players made a $1 bet, choosing as their five basic numbers 22,28,32,33,39 and as their bonus number 40. 21 of these players payed another dollar for the Power Play. The lottery chose the same five basic numbers and 42 for their bonus number and they chose 5 for the power play number. Thus the lottery had to pay 89 of the winners $100,000 and 21 $500,000 dollars for a total of<br />
$19.4 million. <br />
<br />
Power ball officials stated that considering the number of tickets sold in the 29 states the expected 4 or 5 winners. It is not possible to find the number of tickets sold for a given but the probability of getting the fire basic numbers correct and not getting the bonus number is 1/120,526,770 so <br />
</blockquote><br />
The article quotes Chuck Strutt, executive director of the Multi-State Lottery Association as saying:<br />
<blockquote><br />
Panic began at 11:30 pm. March 30 when he got a call from a worred staff member. We didn't sleep a lot that nigh. Is there someone trying to cheat the system?<br />
</blockquote><br />
<br />
Then tried a number of theories about the way people choose their numbers. For example the like geometric designs on the ticket when they pick their numbers. Nothing worked but their first three winners said they had gotten the numbers from a fortune cookie. With this lead they just had to find the fortune cookie maker who had the winning numbers. The found that many different brands of fortune cookes come from the same Long Island City factory, owned by Wonton Food which turns out four million a day. When shown the numbers Derrick Wong, of Wonton Food verified that they had used these numbers. The numbers were chosen from a boal but the company plans to switch to having them chosen by a computer.<br />
<br />
The article states that the Lottery keeps a $25 million reserve for odd situations. They also have further protections agains events like this one. On the back of the ticket we read<br />
<blockquote><br />
In unusual circumstances, the set prize amoount may be paid on a pari-mutual basis which will be lower than the published prize amounts.</div>Laurie Snell